Bulletin of the London Mathematical Society最新文献

{"title":"Monotonicity of the period and positive periodic solutions of a quasilinear equation","authors":"Jean Dolbeault,&nbsp;Marta García-Huidobro,&nbsp;Raúl Manásevich","doi":"10.1112/blms.70315","DOIUrl":"https://doi.org/10.1112/blms.70315","url":null,"abstract":"<p>We investigate the monotonicity of the minimal period of periodic solutions of quasilinear differential equations involving the <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-Laplace operator. First, the monotonicity of the period is obtained as a function of a Hamiltonian energy in two cases. We extend to <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>⩾</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$pgeqslant 2$</annotation>\u0000 </semantics></math> classical results due to Chow–Wang and Chicone for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>=</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$p=2$</annotation>\u0000 </semantics></math>. Then, we consider a differential equation associated with a fundamental interpolation inequality in Sobolev spaces. In that case, we generalize monotonicity results by Miyamoto–Yagasaki and Benguria–Depassier–Loss to <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>⩾</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$pgeqslant 2$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 3","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147562714","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Zarankiewicz bounds from distal regularity lemma","authors":"Mervyn Tong","doi":"10.1112/blms.70310","DOIUrl":"https://doi.org/10.1112/blms.70310","url":null,"abstract":"<p>Since Kővári, Sós and Turán proved upper bounds for the Zarankiewicz problem in 1954, much work has been undertaken to improve these bounds, and some have done so by restricting to particular classes of graphs. In 2017, Fox, Pach, Sheffer, Suk and Zahl proved better bounds for semialgebraic binary relations, and this work was extended by Do in the following year to arbitrary semialgebraic relations. In this paper, we show that Zarankiewicz bounds in the shape of Do's are enjoyed by all relations satisfying the distal regularity lemma, an improved version of the Szemerédi regularity lemma satisfied by relations definable in distal structures (a vast generalisation of o-minimal structures).</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 3","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70310","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147562716","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Poisson kernels on the half-plane are bell-shaped","authors":"Mateusz Kwaśnicki","doi":"10.1112/blms.70303","DOIUrl":"https://doi.org/10.1112/blms.70303","url":null,"abstract":"<p>Consider a second-order elliptic operator <span></span><math>\u0000 <semantics>\u0000 <mi>L</mi>\u0000 <annotation>$L$</annotation>\u0000 </semantics></math> in the half-plane <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>R</mi>\u0000 <mo>×</mo>\u0000 <mo>(</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mi>∞</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathbb {R}times (0, infty)$</annotation>\u0000 </semantics></math> with coefficients depending only on the second coordinate. The Poisson kernel for <span></span><math>\u0000 <semantics>\u0000 <mi>L</mi>\u0000 <annotation>$L$</annotation>\u0000 </semantics></math> is used in the representation of positive <span></span><math>\u0000 <semantics>\u0000 <mi>L</mi>\u0000 <annotation>$L$</annotation>\u0000 </semantics></math>-harmonic functions, that is, solutions of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 <mi>u</mi>\u0000 <mo>=</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$L u = 0$</annotation>\u0000 </semantics></math>. In probabilistic terms, the Poisson kernel is the density function of the distribution of the diffusion in <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>R</mi>\u0000 <mo>×</mo>\u0000 <mo>(</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mi>∞</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathbb {R}times (0, infty)$</annotation>\u0000 </semantics></math> with generator <span></span><math>\u0000 <semantics>\u0000 <mi>L</mi>\u0000 <annotation>$L$</annotation>\u0000 </semantics></math> at the hitting time of the boundary. We prove that the Poisson kernel for <span></span><math>\u0000 <semantics>\u0000 <mi>L</mi>\u0000 <annotation>$L$</annotation>\u0000 </semantics></math> is bell-shaped: its <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>th derivative changes sign <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math> times. In particular, it is unimodal and it has two inflection points (it is concave, then convex and then concave again).</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 3","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147569664","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A note on a diffeomorphism criterion via long-time Ricci flow","authors":"Shaochuang Huang,&nbsp;Zhuo Peng","doi":"10.1112/blms.70321","DOIUrl":"https://doi.org/10.1112/blms.70321","url":null,"abstract":"<p>In this note, we give a diffeomorphism (to <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <annotation>$mathbb {R}^n$</annotation>\u0000 </semantics></math>) criterion via long-time Ricci flow and show some applications. In particular, we provide an affirmative answer that the conclusion in Chan, Huang, and Lee [Ann. PDE <b>10</b> (2024), no. 2, Paper No. 23, 31] and Martens [Bull. London Math. Soc. <b>57</b> (2025), no. 7, 1968–1989] about manifolds with small curvature concentration can be improved to diffeomorphism in dimension 4.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 3","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147569665","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Poset topology, moves, and Bruhat interval polytope lattices","authors":"Christian Gaetz,&nbsp;Patricia Hersh","doi":"10.1112/blms.70309","DOIUrl":"https://doi.org/10.1112/blms.70309","url":null,"abstract":"<p>We study the poset topology of lattices arising from orientations of 1-skeleta of <i>directionally simple</i> polytopes, with Bruhat interval polytopes <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>Q</mi>\u0000 <mrow>\u0000 <mi>e</mi>\u0000 <mo>,</mo>\u0000 <mi>w</mi>\u0000 </mrow>\u0000 </msub>\u0000 <annotation>$Q_{e,w}$</annotation>\u0000 </semantics></math> as our main example. We show that the order complex <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Δ</mi>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>u</mi>\u0000 <mo>,</mo>\u0000 <mi>v</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mi>w</mi>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$Delta ((u,v)_w)$</annotation>\u0000 </semantics></math> of an interval therein is homotopy equivalent to a sphere if <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>Q</mi>\u0000 <mrow>\u0000 <mi>u</mi>\u0000 <mo>,</mo>\u0000 <mi>v</mi>\u0000 </mrow>\u0000 </msub>\u0000 <annotation>$Q_{u,v}$</annotation>\u0000 </semantics></math> is a face of <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>Q</mi>\u0000 <mrow>\u0000 <mi>e</mi>\u0000 <mo>,</mo>\u0000 <mi>w</mi>\u0000 </mrow>\u0000 </msub>\u0000 <annotation>$Q_{e,w}$</annotation>\u0000 </semantics></math> and is otherwise contractible. This significantly generalizes the known case of the permutahedron. We also show that saturated chains from <span></span><math>\u0000 <semantics>\u0000 <mi>u</mi>\u0000 <annotation>$u$</annotation>\u0000 </semantics></math> to <span></span><math>\u0000 <semantics>\u0000 <mi>v</mi>\u0000 <annotation>$v$</annotation>\u0000 </semantics></math> in such lattices are connected, and in fact highly connected, under flipping across 2-faces. When <span></span><math>\u0000 <semantics>\u0000 <mi>w</mi>\u0000 <annotation>$w$</annotation>\u0000 </semantics></math> is a Grassmannian permutation, this implies a strengthening of the restriction of Postnikov's move-equivalence theorem to the class of BCFW bridge decomposable plabic graphs.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 3","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147569776","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bi-orderability and generalized torsion elements from the perspective of profinite properties","authors":"Wonyong Jang,&nbsp;Junseok Kim","doi":"10.1112/blms.70308","DOIUrl":"https://doi.org/10.1112/blms.70308","url":null,"abstract":"<p>Using fiber products, we construct bi-orderable groups from left-orderable groups. As an application, we show that bi-orderability is not a profinite property, answering a question of Piwek and Wykowski negatively. We also show that the existence of a generalized torsion element is not a profinite property.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 3","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147569115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Groups with conjugacy classes of coprime sizes","authors":"R. D. Camina,&nbsp;A. Maróti,&nbsp;E. Pacifici,&nbsp;C. Parker,&nbsp;K. Rekvényi,&nbsp;J. Saunders,&nbsp;V. Sotomayor,&nbsp;G. Tracey,&nbsp;M. van Beek","doi":"10.1112/blms.70320","DOIUrl":"https://doi.org/10.1112/blms.70320","url":null,"abstract":"&lt;p&gt;Suppose that &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;annotation&gt;$x$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;y&lt;/mi&gt;\u0000 &lt;annotation&gt;$y$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; are elements of a finite group &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;annotation&gt;$G$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; lying in conjugacy classes of coprime sizes. We prove that &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;⟨&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;⟩&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;∩&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;⟨&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;y&lt;/mi&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;⟩&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$langle x^G rangle cap langle y^G rangle$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is an abelian normal subgroup of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;annotation&gt;$G$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and, as a consequence, that if &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;annotation&gt;$x$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;y&lt;/mi&gt;\u0000 &lt;annotation&gt;$y$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; are &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;π&lt;/mi&gt;\u0000 &lt;annotation&gt;$pi$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-regular elements for some set of primes &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;π&lt;/mi&gt;\u0000 &lt;annotation&gt;$pi$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, then &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;y&lt;/mi&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$x^G y^G$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is a &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;π&lt;/mi&gt;\u0000 &lt;annotation&gt;$pi$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-regular conjugacy class in &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;a","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 3","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70320","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147569112","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hilbert–Kunz multiplicity and F-signature can disagree","authors":"Seungsu Lee,&nbsp;Suchitra Pande,&nbsp;Austyn Simpson","doi":"10.1112/blms.70304","DOIUrl":"https://doi.org/10.1112/blms.70304","url":null,"abstract":"&lt;p&gt;We compute the &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;annotation&gt;$F$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-signature function of the ample cone of any nontrivial ruled surface over &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mi&gt;P&lt;/mi&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;annotation&gt;$mathbb {P}^1_k$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, where &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;annotation&gt;$k$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is an algebraically closed field of prime characteristic. As an application, we construct a Noetherian &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;annotation&gt;$F$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-finite strongly &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;annotation&gt;$F$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-regular ring &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;annotation&gt;$R$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of prime characteristic admitting two maximal ideals &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mo&gt;Spec&lt;/mo&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$mathfrak {n}_1,mathfrak {n}_2in operatorname{Spec}R$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; at which the Hilbert–Kunz multiplicity and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;annotation&gt;$F$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-signature measure different singularities; that is, &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mo&gt;e&lt;/mo&gt;\u0000 &lt;mo&gt;HK&lt;/mo&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mo&gt;e&lt;/mo&gt;\u0000 &lt;mo&gt;HK&lt;/mo&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 ","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 3","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147569111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On \u0000 \u0000 ℓ\u0000 $ell$\u0000 -open and \u0000 \u0000 ℓ\u0000 $ell$\u0000 -closed \u0000 \u0000 \u0000 C\u0000 ∗\u0000 \u0000 $C^*$\u0000 -algebras","authors":"Dolapo Oyetunbi,&nbsp;Aaron Tikuisis","doi":"10.1112/blms.70306","DOIUrl":"https://doi.org/10.1112/blms.70306","url":null,"abstract":"<p>In this paper, we characterize <span></span><math>\u0000 <semantics>\u0000 <mi>ℓ</mi>\u0000 <annotation>$ell$</annotation>\u0000 </semantics></math>-open and <span></span><math>\u0000 <semantics>\u0000 <mi>ℓ</mi>\u0000 <annotation>$ell$</annotation>\u0000 </semantics></math>-closed <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation>$C^*$</annotation>\u0000 </semantics></math>-algebras and deduce that <span></span><math>\u0000 <semantics>\u0000 <mi>ℓ</mi>\u0000 <annotation>$ell$</annotation>\u0000 </semantics></math>-open <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation>$C^*$</annotation>\u0000 </semantics></math>-algebras are <span></span><math>\u0000 <semantics>\u0000 <mi>ℓ</mi>\u0000 <annotation>$ell$</annotation>\u0000 </semantics></math>-closed, as conjectured by Blackadar. Moreover, we show that a commutative unital <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation>$C^*$</annotation>\u0000 </semantics></math>-algebra is <span></span><math>\u0000 <semantics>\u0000 <mi>ℓ</mi>\u0000 <annotation>$ell$</annotation>\u0000 </semantics></math>-open if and only if it is semiprojective.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 3","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147568690","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On universal-homogeneous hyperbolic graphs and spaces and their isometry groups","authors":"Katrin Tent","doi":"10.1112/blms.70307","DOIUrl":"https://doi.org/10.1112/blms.70307","url":null,"abstract":"&lt;p&gt;The Urysohn space is the unique separable metric space that is universal and homogeneous for finite metric spaces, that is, it embeds any finite metric space any isometry between finite subspaces extends to an isometry of the whole space. We here consider the existence of a universal-homogeneous hyperbolic space. We show that for &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;δ&lt;/mi&gt;\u0000 &lt;mo&gt;&gt;&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$delta &gt;0$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; there is no &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;δ&lt;/mi&gt;\u0000 &lt;annotation&gt;$delta$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-hyperbolic space which is universal and homogeneous in the above sense for all finite &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;δ&lt;/mi&gt;\u0000 &lt;annotation&gt;$delta$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-hpyerbolic spaces. We then show that for any &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;δ&lt;/mi&gt;\u0000 &lt;mo&gt;⩾&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$delta geqslant 0$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and any countable class &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;annotation&gt;$mathcal {C}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;δ&lt;/mi&gt;\u0000 &lt;annotation&gt;$delta$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-hyperbolic spaces with countably many distinguished &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;δ&lt;/mi&gt;\u0000 &lt;annotation&gt;$delta$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-closed subspaces there exists a &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;δ&lt;/mi&gt;\u0000 &lt;annotation&gt;$delta$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-hyperbolic metric space &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;δ&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$mathbb {H}_mathcal {C}=mathbb {H}(mathcal {C},delta)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; such that every &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;m","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 3","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70307","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147568692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}