Journal of the London Mathematical Society-Second Series最新文献

{"title":"Closed 3-forms in five dimensions and embedding problems","authors":"Simon Donaldson,&nbsp;Fabian Lehmann","doi":"10.1112/jlms.12897","DOIUrl":"https://doi.org/10.1112/jlms.12897","url":null,"abstract":"<p>We consider the question if a five-dimensional manifold can be embedded into a Calabi–Yau manifold of complex dimension 3 such that the real part of the holomorphic volume form induces a given closed 3-form on the 5-manifold. We define an open set of 3-forms in dimension five which we call strongly pseudoconvex, and show that for closed strongly pseudoconvex 3-forms, the perturbative version of this embedding problem can be solved if a finite-dimensional vector space of obstructions vanishes.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12897","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140351624","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Gravitational instantons with quadratic volume growth","authors":"Gao Chen,&nbsp;Jeff Viaclovsky","doi":"10.1112/jlms.12886","DOIUrl":"https://doi.org/10.1112/jlms.12886","url":null,"abstract":"<p>There are two known classes of gravitational instantons with quadratic volume growth at infinity, known as type <span></span><math>\u0000 <semantics>\u0000 <mo>ALG</mo>\u0000 <annotation>$operatorname{ALG}$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mo>ALG</mo>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation>$operatorname{ALG}^*$</annotation>\u0000 </semantics></math>. Gravitational instantons of type <span></span><math>\u0000 <semantics>\u0000 <mo>ALG</mo>\u0000 <annotation>$operatorname{ALG}$</annotation>\u0000 </semantics></math> were previously classified by Chen–Chen. In this paper, we prove a classification theorem for <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>ALG</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation>${rm ALG}^*$</annotation>\u0000 </semantics></math> gravitational instantons. We determine the topology and prove existence of “uniform” coordinates at infinity for both ALG and <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>ALG</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation>${rm ALG}^*$</annotation>\u0000 </semantics></math> gravitational instantons. We also prove a result regarding the relationship between ALG gravitational instantons of order <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$mathfrak {n}$</annotation>\u0000 </semantics></math> and those of order 2.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12886","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140331179","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A notion of seminormalization for real algebraic varieties","authors":"François Bernard","doi":"10.1112/jlms.12891","DOIUrl":"https://doi.org/10.1112/jlms.12891","url":null,"abstract":"<p>The seminormalization of an algebraic variety <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> is the biggest variety linked to <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> by a finite, birational, and bijective morphism. In this paper, we introduce a variant of the seminormalization, suited for real algebraic varieties, called the R-seminormalization. This object has a universal property of the same kind as the one of the seminormalization but related to the real closed points of the variety. In a previous paper, the author studied the seminormalization of complex algebraic varieties using rational functions that extend continuously to the closed points for the Euclidean topology. We adapt some of those results here to the R-seminormalization, and we provide several examples. We also show that the R-seminormalization modifies the singularities of a real variety by normalizing the purely complex points and seminormalizing the real ones.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12891","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140329036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Commuting tuple of multiplication operators homogeneous under the unitary group","authors":"Soumitra Ghara,&nbsp;Surjit Kumar,&nbsp;Gadadhar Misra,&nbsp;Paramita Pramanick","doi":"10.1112/jlms.12890","DOIUrl":"https://doi.org/10.1112/jlms.12890","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>U</mi>\u0000 <mo>(</mo>\u0000 <mi>d</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathcal {U}(d)$</annotation>\u0000 </semantics></math> be the group of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 <mo>×</mo>\u0000 <mi>d</mi>\u0000 </mrow>\u0000 <annotation>$dtimes d$</annotation>\u0000 </semantics></math> unitary matrices. We find conditions to ensure that a <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>U</mi>\u0000 <mo>(</mo>\u0000 <mi>d</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathcal {U}(d)$</annotation>\u0000 </semantics></math>-homogeneous <span></span><math>\u0000 <semantics>\u0000 <mi>d</mi>\u0000 <annotation>$d$</annotation>\u0000 </semantics></math>-tuple <span></span><math>\u0000 <semantics>\u0000 <mi>T</mi>\u0000 <annotation>$bm{T}$</annotation>\u0000 </semantics></math> is unitarily equivalent to multiplication by the coordinate functions on some reproducing kernel Hilbert space <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>H</mi>\u0000 <mi>K</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>B</mi>\u0000 <mi>d</mi>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>⊆</mo>\u0000 <mtext>Hol</mtext>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>B</mi>\u0000 <mi>d</mi>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$mathcal {H}_K(mathbb {B}_d, mathbb {C}^n) subseteq mbox{rm Hol}(mathbb {B}_d, mathbb {C}^n)$</annotation>\u0000 </semantics></math>, <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>=</mo>\u0000 <mo>dim</mo>\u0000 <msubsup>\u0000 <mo>∩</mo>\u0000 <mrow>\u0000 <mi>j</mi>\u0000 <mo>=</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <mi>d</mi>\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140321787","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On local stability threshold of del Pezzo surfaces","authors":"Erroxe Etxabarri-Alberdi","doi":"10.1112/jlms.12887","DOIUrl":"https://doi.org/10.1112/jlms.12887","url":null,"abstract":"<p>We complete the classification of local stability thresholds for smooth del Pezzo surfaces of degree 2. In particular, we show that this number is irrational if and only if there is a unique (-1)-curve passing through the point where we are computing the local invariant.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12887","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140310291","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Genus 0 logarithmic and tropical fixed-domain counts for Hirzebruch surfaces","authors":"Alessio Cela,&nbsp;Aitor Iribar López","doi":"10.1112/jlms.12892","DOIUrl":"https://doi.org/10.1112/jlms.12892","url":null,"abstract":"<p>For a non-singular projective toric variety <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math>, the virtual logarithmic Tevelev degrees are defined as the virtual degree of the morphism from the moduli stack of logarithmic stable maps <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mover>\u0000 <mi>M</mi>\u0000 <mo>¯</mo>\u0000 </mover>\u0000 <mi>Γ</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>X</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$overline{mathcal {M}}_{mathsf {Gamma }}(X)$</annotation>\u0000 </semantics></math> to the product <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mover>\u0000 <mi>M</mi>\u0000 <mo>¯</mo>\u0000 </mover>\u0000 <mrow>\u0000 <mi>g</mi>\u0000 <mo>,</mo>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mo>×</mo>\u0000 <msup>\u0000 <mi>X</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$overline{mathcal {M}}_{g,n} times X^n$</annotation>\u0000 </semantics></math>. In this paper, after proving that Mikhalkin's correspondence theorem holds in genus 0 for logarithmic virtual Tevelev degrees, we use tropical methods to provide closed formulas for the case in which <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> is a Hirzebruch surface. In order to do so, we explicitly list all the tropical curves contributing to the count.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12892","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140297273","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Solutions of the \u0000 \u0000 \u0000 sl\u0000 2\u0000 \u0000 ${mathfrak {sl}_2}$\u0000 qKZ equations modulo an integer","authors":"Evgeny Mukhin,&nbsp;Alexander Varchenko","doi":"10.1112/jlms.12884","DOIUrl":"https://doi.org/10.1112/jlms.12884","url":null,"abstract":"<p>We study the <i>qKZ</i> difference equations with values in the <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>th tensor power of the vector <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>sl</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <annotation>${mathfrak {sl}_2}$</annotation>\u0000 </semantics></math> representation <span></span><math>\u0000 <semantics>\u0000 <mi>V</mi>\u0000 <annotation>$V$</annotation>\u0000 </semantics></math>, variables <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>z</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <mi>⋯</mi>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>z</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$z_1,dots,z_n$</annotation>\u0000 </semantics></math>, and integer step <span></span><math>\u0000 <semantics>\u0000 <mi>κ</mi>\u0000 <annotation>$kappa$</annotation>\u0000 </semantics></math>. For any integer <span></span><math>\u0000 <semantics>\u0000 <mi>N</mi>\u0000 <annotation>$N$</annotation>\u0000 </semantics></math> relatively prime to the step <span></span><math>\u0000 <semantics>\u0000 <mi>κ</mi>\u0000 <annotation>$kappa$</annotation>\u0000 </semantics></math>, we construct a family of polynomials <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>f</mi>\u0000 <mi>r</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>z</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$f_r(z)$</annotation>\u0000 </semantics></math> in variables <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>z</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <mi>⋯</mi>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>z</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$z_1,dots,z_n$</annotation>\u0000 </semantics></math> with values in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>V</mi>\u0000 <mrow>\u0000 <mo>⊗</mo>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>$V^{otimes n}$</annotation>\u0000 </semantics></math> such that the coordinates of the","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140297257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The \u0000 \u0000 \u0000 ℓ\u0000 p\u0000 \u0000 $ell ^p$\u0000 norm of the Riesz–Titchmarsh transform for even integer \u0000 \u0000 p\u0000 $p$","authors":"Rodrigo Bañuelos,&nbsp;Mateusz Kwaśnicki","doi":"10.1112/jlms.12888","DOIUrl":"https://doi.org/10.1112/jlms.12888","url":null,"abstract":"<p>The long-standing conjecture that for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>∈</mo>\u0000 <mo>(</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mi>∞</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$p in (1, infty)$</annotation>\u0000 </semantics></math> the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>ℓ</mi>\u0000 <mi>p</mi>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>Z</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$ell ^p(mathbb {Z})$</annotation>\u0000 </semantics></math> norm of the Riesz–Titchmarsh discrete Hilbert transform is the same as the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>p</mi>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>R</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$L^p(mathbb {R})$</annotation>\u0000 </semantics></math> norm of the classical Hilbert transform, is verified when <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>=</mo>\u0000 <mn>2</mn>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <annotation>$p = 2 n$</annotation>\u0000 </semantics></math> or <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mfrac>\u0000 <mi>p</mi>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </mfrac>\u0000 <mo>=</mo>\u0000 <mn>2</mn>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <annotation>$frac{p}{p - 1} = 2 n$</annotation>\u0000 </semantics></math>, for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>∈</mo>\u0000 <mi>N</mi>\u0000 </mrow>\u0000 <annotation>$n in mathbb {N}$</annotation>\u0000 </semantics></math>. The proof, which is algebraic in nature, depends in a crucial way on the sharp estimate for the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>ℓ</mi>\u0000 <mi>p</mi>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>Z</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140297272","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An interpolation inequality involving \u0000 \u0000 \u0000 L\u0000 log\u0000 L\u0000 \u0000 $Llog L$\u0000 spaces and application to the characterization of blow-up behavior in a two-dimensional Keller–Segel–Navier–Stokes system","authors":"Yulan Wang,&nbsp;Michael Winkler","doi":"10.1112/jlms.12885","DOIUrl":"10.1112/jlms.12885","url":null,"abstract":"<p>In a smoothly bounded two-dimensional domain <math>\u0000 <semantics>\u0000 <mi>Ω</mi>\u0000 <annotation>$Omega$</annotation>\u0000 </semantics></math> and for a given nondecreasing positive unbounded <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ℓ</mi>\u0000 <mo>∈</mo>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mn>0</mn>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mrow>\u0000 <mo>[</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mi>∞</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$ell in C^0([0,infty))$</annotation>\u0000 </semantics></math>, for each <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>K</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$K&amp;gt;0$</annotation>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>η</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$eta &amp;gt;0$</annotation>\u0000 </semantics></math> the inequality\u0000\u0000 </p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12885","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140072441","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Incommensurable lattices in Baumslag–Solitar complexes","authors":"Max Forester","doi":"10.1112/jlms.12879","DOIUrl":"https://doi.org/10.1112/jlms.12879","url":null,"abstract":"<p>This paper concerns locally finite 2-complexes <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>X</mi>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 <mo>,</mo>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msub>\u0000 <annotation>$X_{m,n}$</annotation>\u0000 </semantics></math> that are combinatorial models for the Baumslag–Solitar groups <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>B</mi>\u0000 <mi>S</mi>\u0000 <mo>(</mo>\u0000 <mi>m</mi>\u0000 <mo>,</mo>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$BS(m,n)$</annotation>\u0000 </semantics></math>. We show that, in many cases, the locally compact group <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>Aut</mo>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>X</mi>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 <mo>,</mo>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$operatorname{Aut}(X_{m,n})$</annotation>\u0000 </semantics></math> contains incommensurable uniform lattices. The lattices we construct also admit isomorphic Cayley graphs and are finitely presented, torsion-free, and coherent.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140066500","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}