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Groups with a finite Busemann boundary are virtually cyclic 具有有限Busemann边界的群实际上是循环的
IF 1 3区 数学
Bulletin of the London Mathematical Society Pub Date : 2026-07-24 DOI: 10.1112/blms.70462
Corentin Bodart, Liran Ron-George, Ariel Yadin
{"title":"Groups with a finite Busemann boundary are virtually cyclic","authors":"Corentin Bodart,&nbsp;Liran Ron-George,&nbsp;Ariel Yadin","doi":"10.1112/blms.70462","DOIUrl":"https://doi.org/10.1112/blms.70462","url":null,"abstract":"<p>This note is a continuation of the study of the relationship between the geometry of Cayley graphs and the size of its metric-functional boundary. We show that if there exists a Cayley graph with finitely many Busemann points, then the underlying group is virtually cyclic. Together with previous works, this completes the full characterization of groups with finite metric-functional boundaries. The main new notion introduced is that of <i>annihilators</i>.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 8","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70462","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148615802","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}
引用次数: 0
On a Ramsey–Turán variant of Roth's theorem 关于Roth定理的Ramsey-Turán变体
IF 1 3区 数学
Bulletin of the London Mathematical Society Pub Date : 2026-07-24 DOI: 10.1112/blms.70436
Matija Bucić, Micha Christoph, Jaehoon Kim, Hyunwoo Lee, Varun Sivashankar
{"title":"On a Ramsey–Turán variant of Roth's theorem","authors":"Matija Bucić,&nbsp;Micha Christoph,&nbsp;Jaehoon Kim,&nbsp;Hyunwoo Lee,&nbsp;Varun Sivashankar","doi":"10.1112/blms.70436","DOIUrl":"https://doi.org/10.1112/blms.70436","url":null,"abstract":"<p>A classical theorem of Roth states that the maximum size of a solution-free set of a homogeneous linear equation <span></span><math>\u0000 <semantics>\u0000 <mi>L</mi>\u0000 <annotation>$mathcal {L}$</annotation>\u0000 </semantics></math> in <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>F</mi>\u0000 <mi>p</mi>\u0000 </msub>\u0000 <annotation>$mathbb {F}_p$</annotation>\u0000 </semantics></math> is <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>o</mi>\u0000 <mo>(</mo>\u0000 <mi>p</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$o(p)$</annotation>\u0000 </semantics></math> if and only if the sum of the coefficients of <span></span><math>\u0000 <semantics>\u0000 <mi>L</mi>\u0000 <annotation>$mathcal {L}$</annotation>\u0000 </semantics></math> is 0. In this paper, we prove a Ramsey–Turán variant of Roth's theorem, with respect to a natural notion of “structured” sets introduced by Erdős and Sárközy in the 1970s. Namely, we show that the following statements are equivalent: \u0000\u0000 </p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 8","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70436","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148615789","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}
引用次数: 0
Totally elliptic surface group representations 全椭圆曲面群表示
IF 1 3区 数学
Bulletin of the London Mathematical Society Pub Date : 2026-07-23 DOI: 10.1112/blms.70455
Arnaud Maret
{"title":"Totally elliptic surface group representations","authors":"Arnaud Maret","doi":"10.1112/blms.70455","DOIUrl":"https://doi.org/10.1112/blms.70455","url":null,"abstract":"<p>A surface group representation into a Lie group is totally elliptic if every simple closed curve on the surface is mapped to an elliptic element. In this note, we characterize all totally elliptic surface group representations into <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mo>PSL</mo>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 <annotation>$operatorname{PSL}_2 mathbb {R}$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mo>PSL</mo>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <mi>C</mi>\u0000 </mrow>\u0000 <annotation>$operatorname{PSL}_2mathbb {C}$</annotation>\u0000 </semantics></math> by showing that they are either representations into a compact subgroup or Deroin–Tholozan representations.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 8","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70455","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148615463","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}
引用次数: 0
On the positivity and integrality of coefficients of mirror maps 关于镜像映射系数的正性和完整性
IF 1 3区 数学
Bulletin of the London Mathematical Society Pub Date : 2026-07-23 DOI: 10.1112/blms.70350
Sophie Bleau, Nick Sheridan
{"title":"On the positivity and integrality of coefficients of mirror maps","authors":"Sophie Bleau,&nbsp;Nick Sheridan","doi":"10.1112/blms.70350","DOIUrl":"https://doi.org/10.1112/blms.70350","url":null,"abstract":"<p>We present natural conjectural generalisations of the ‘positivity and integrality of mirror maps’ phenomenon, encompassing the mirror maps appearing in the Batyrev–Borisov construction of mirror Calabi–Yau complete intersections in Fano toric varieties as a special case. We find that, given the combinatorial data from which one constructs a mirror pair of Calabi–Yau complete intersections, there are <i>two</i> ways of writing down an associated ‘mirror map’: one which is the ‘true mirror map’, meaning the one which appears in mirror symmetry theorems; and one which is the ‘naive mirror map’. The two are equal under a certain combinatorial criterion which holds, for example, for the quintic threefold, but not in general. We conjecture (based on substantial computer checks, together with proofs under extra hypotheses) that the naive mirror map always has positive integer coefficients, while the true mirror map always has integer (but not necessarily positive) coefficients. Most previous works on the integrality of mirror maps concern the naive mirror map, and in particular, only apply to the true mirror map under the combinatorial criterion mentioned above.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 8","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70350","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148615465","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}
引用次数: 0
On Nielsen equivalence classes of two-element generators of mapping class groups 映射类群的二元生成器的Nielsen等价类
IF 1 3区 数学
Bulletin of the London Mathematical Society Pub Date : 2026-07-23 DOI: 10.1112/blms.70454
Susumu Hirose, Naoyuki Monden
{"title":"On Nielsen equivalence classes of two-element generators of mapping class groups","authors":"Susumu Hirose,&nbsp;Naoyuki Monden","doi":"10.1112/blms.70454","DOIUrl":"https://doi.org/10.1112/blms.70454","url":null,"abstract":"<p>We show that there are infinitely many Nielsen equivalence classes of the mapping class group of a closed oriented surface of genus at least eight.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 8","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70454","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148615834","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}
引用次数: 0
Kitaoka's conjecture and sums of squares 北冈猜想与平方和
IF 1 3区 数学
Bulletin of the London Mathematical Society Pub Date : 2026-07-20 DOI: 10.1112/blms.70445
Vítězslav Kala, Kristýna Kramer, Jakub Krásenský
{"title":"Kitaoka's conjecture and sums of squares","authors":"Vítězslav Kala,&nbsp;Kristýna Kramer,&nbsp;Jakub Krásenský","doi":"10.1112/blms.70445","DOIUrl":"https://doi.org/10.1112/blms.70445","url":null,"abstract":"<p>We connect the existence of a ternary classical universal quadratic form over a totally real number field <span></span><math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math> with the property that all totally positive multiples of 2 are sums of squares (if <span></span><math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math> does not contain <span></span><math>\u0000 <semantics>\u0000 <msqrt>\u0000 <mn>2</mn>\u0000 </msqrt>\u0000 <annotation>$sqrt{2}$</annotation>\u0000 </semantics></math> or contains a nonsquare totally positive unit). In particular, we get that Kitaoka's conjecture holds for all fields of odd discriminant.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 8","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70445","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148534137","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}
引用次数: 0
Pointwise ergodic averages along the omega function in number fields 沿着函数在数域中的点遍历平均
IF 1 3区 数学
Bulletin of the London Mathematical Society Pub Date : 2026-07-20 DOI: 10.1112/blms.70450
Diego Céspedes, Sebastián Donoso
{"title":"Pointwise ergodic averages along the omega function in number fields","authors":"Diego Céspedes,&nbsp;Sebastián Donoso","doi":"10.1112/blms.70450","DOIUrl":"https://doi.org/10.1112/blms.70450","url":null,"abstract":"<p>We study a general criterion for guaranteeing that an ergodic average exhibits the strong sweeping-out property. This result implies, in particular, the failure of pointwise convergence of these averages. Our result applies to averages along the Omega function in number fields, generalizing a result of Loyd. We also show that the averages\u0000\u0000 </p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 8","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148534201","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}
引用次数: 0
Finiteness of the Hölder–Brascamp–Lieb constant revisited 重新审视Hölder-Brascamp-Lieb常数的有限性
IF 1 3区 数学
Bulletin of the London Mathematical Society Pub Date : 2026-07-19 DOI: 10.1112/blms.70451
Philip T. Gressman
{"title":"Finiteness of the Hölder–Brascamp–Lieb constant revisited","authors":"Philip T. Gressman","doi":"10.1112/blms.70451","DOIUrl":"https://doi.org/10.1112/blms.70451","url":null,"abstract":"<p>Abstract Hölder–Brascamp–Lieb inequalities have become a ubiquitous tool in Fourier analysis in recent years, due in large part to a theorem of Bennett et al. characterizing finiteness of the Hölder–Brascamp–Lieb constant. Here we provide a new characterization of a substantially different nature involving directed graphs of subspaces. Its practical value derives from its complementary nature to the Bennett et al. conditions: it creates a means by which one can establish finiteness of the Hölder–Brascamp–Lieb constant by analysis of a well-chosen, finite list of subspaces rather than by checking conditions on all subspaces of the underlying vector space. The proof is elementary and is essentially an “explicitization” of the semi-explicit factorization algorithm of Carbery et al.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 8","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70451","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148534233","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}
引用次数: 0
A small remark on small-dimensional normed barreled spaces 关于小维赋范桶空间的一个小注释
IF 1 3区 数学
Bulletin of the London Mathematical Society Pub Date : 2026-07-14 DOI: 10.1112/blms.70431
Damian Sobota
{"title":"A small remark on small-dimensional normed barreled spaces","authors":"Damian Sobota","doi":"10.1112/blms.70431","DOIUrl":"https://doi.org/10.1112/blms.70431","url":null,"abstract":"<p>Combining the methods of Brian and Stuart with the classical Dvoretzky theorem, we show that no infinite-dimensional Banach space contains a barreled subspace of (algebraic) dimension <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>&lt;</mo>\u0000 <mtext>cov</mtext>\u0000 <mo>(</mo>\u0000 <mi>N</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$&lt;mbox{cov}(mathcal {N})$</annotation>\u0000 </semantics></math>, the covering number of the Lebesgue null ideal <span></span><math>\u0000 <semantics>\u0000 <mi>N</mi>\u0000 <annotation>$mathcal {N}$</annotation>\u0000 </semantics></math>. Consequently, every infinite-dimensional normed barreled space has dimension <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>⩾</mo>\u0000 <mtext>cov</mtext>\u0000 <mo>(</mo>\u0000 <mi>N</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$geqslant mbox{cov}(mathcal {N})$</annotation>\u0000 </semantics></math> and so it is consistent with <span>ZFC</span> that no normed barreled space has dimension equal to the bounding number <span></span><math>\u0000 <semantics>\u0000 <mi>b</mi>\u0000 <annotation>$mathfrak {b}$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 7","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70431","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148467491","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}
引用次数: 0
Simple normal crossing Kähler–Einstein metrics and RCD spaces 简单法向交叉Kähler-Einstein指标和RCD空间
IF 1 3区 数学
Bulletin of the London Mathematical Society Pub Date : 2026-07-10 DOI: 10.1112/blms.70443
Martin de Borbon, Cristiano Spotti
{"title":"Simple normal crossing Kähler–Einstein metrics and RCD spaces","authors":"Martin de Borbon,&nbsp;Cristiano Spotti","doi":"10.1112/blms.70443","DOIUrl":"https://doi.org/10.1112/blms.70443","url":null,"abstract":"<p>We show that Kähler–Einstein metrics with cone singularities along simple normal crossing (SNC) divisors define Riemannian Curvature Dimension (RCD) spaces, both in the compact setting and in certain non-compact cases, thereby producing many examples of Einstein RCD spaces. In particular, we show the existence of smooth non-compact 4-manifolds carrying Asymptotically Locally Euclidean (ALE). Ricci-flat RCD(0,4) metrics with <i>any</i> space form <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mn>3</mn>\u0000 </msup>\u0000 <mo>/</mo>\u0000 <mi>Γ</mi>\u0000 </mrow>\u0000 <annotation>$S^3/Gamma$</annotation>\u0000 </semantics></math> as the link of the tangent cone at infinity, answering a question raised by Semola. Our proofs rely on the characterization of RCD spaces in the almost-smooth setting due to Honda and Honda–Sun.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 7","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70443","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148466836","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}
引用次数: 0
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