{"title":"Non-smoothable homeomorphisms of 4-manifolds with boundary","authors":"Daniel Galvin , Roberto Ladu","doi":"10.1016/j.aim.2025.110191","DOIUrl":"10.1016/j.aim.2025.110191","url":null,"abstract":"<div><div>We construct the first examples of non-smoothable self-homeomorphisms of smooth 4-manifolds with boundary that fix the boundary and act trivially on homology. As a corollary, we construct self-diffeomorphisms of 4-manifolds with boundary that fix the boundary and act trivially on homology but cannot be isotoped to any self-diffeomorphism supported in a collar of the boundary and, in particular, are not isotopic to any generalised Dehn twist.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"467 ","pages":"Article 110191"},"PeriodicalIF":1.5,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143552551","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Affine dual Minkowski problems","authors":"Xiaxing Cai, Gangsong Leng, Yuchi Wu, Dongmeng Xi","doi":"10.1016/j.aim.2025.110184","DOIUrl":"10.1016/j.aim.2025.110184","url":null,"abstract":"<div><div>While affine functionals of convex bodies and their affine isoperimetric inequalities have been extensively studied, the construction of geometric measures arising from affine geometric invariants (other than volume) has been missing.</div><div>In this work, affine ‘‘invariant’’ measures derived from the dual affine quermassintegrals are presented. Minkowski problems for the new affine-invariant measures are proposed and studied. The new variation formula derived here leads to new affine operators that map star bodies to star bodies. An affine isoperimetric inequality is obtained for new bi-dual intersection bodies.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"467 ","pages":"Article 110184"},"PeriodicalIF":1.5,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143552552","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Homological n-systole in (n + 1)-manifolds and bi-Ricci curvature","authors":"Jianchun Chu , Man-Chun Lee , Jintian Zhu","doi":"10.1016/j.aim.2025.110187","DOIUrl":"10.1016/j.aim.2025.110187","url":null,"abstract":"<div><div>In this paper, we prove an optimal systolic inequality and the corresponding rigidity in the equality case on closed manifolds with positive bi-Ricci curvature, which generalizes the work of Bray-Brendle-Neves in <span><span>[3]</span></span>. The proof is given in all dimensions based on the method of minimal surfaces under the Generic Regularity Hypothesis, which is known to be true up to dimension ten.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"467 ","pages":"Article 110187"},"PeriodicalIF":1.5,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143534818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On exponential frames near the critical density","authors":"Marcin Bownik , Jordy Timo van Velthoven","doi":"10.1016/j.aim.2025.110180","DOIUrl":"10.1016/j.aim.2025.110180","url":null,"abstract":"<div><div>Given a relatively compact set <span><math><mi>Ω</mi><mo>⊆</mo><mi>R</mi></math></span> of Lebesgue measure <span><math><mo>|</mo><mi>Ω</mi><mo>|</mo></math></span> and <span><math><mi>ε</mi><mo>></mo><mn>0</mn></math></span>, we show the existence of a set <span><math><mi>Λ</mi><mo>⊆</mo><mi>R</mi></math></span> of uniform density <span><math><mi>D</mi><mo>(</mo><mi>Λ</mi><mo>)</mo><mo>≤</mo><mo>(</mo><mn>1</mn><mo>+</mo><mi>ε</mi><mo>)</mo><mo>|</mo><mi>Ω</mi><mo>|</mo></math></span> such that the exponential system <span><math><mo>{</mo><mi>exp</mi><mo></mo><mo>(</mo><mn>2</mn><mi>π</mi><mi>i</mi><mi>λ</mi><mo>⋅</mo><mo>)</mo><msub><mrow><mn>1</mn></mrow><mrow><mi>Ω</mi></mrow></msub><mo>:</mo><mi>λ</mi><mo>∈</mo><mi>Λ</mi><mo>}</mo></math></span> is a frame for <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>Ω</mi><mo>)</mo></math></span> with frame bounds <span><math><mi>A</mi><mo>|</mo><mi>Ω</mi><mo>|</mo><mo>,</mo><mi>B</mi><mo>|</mo><mi>Ω</mi><mo>|</mo></math></span> for constants <span><math><mi>A</mi><mo>,</mo><mi>B</mi></math></span> only depending on <em>ε</em>. This solves a problem on the frame bounds of an exponential frame near the critical density posed by Nitzan, Olevskii and Ulanovskii. We also prove an extension to locally compact abelian groups, which improves a result by Agora, Antezana and Cabrelli by providing frame bounds involving the spectrum.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"467 ","pages":"Article 110180"},"PeriodicalIF":1.5,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143528959","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Level set estimates for the periodic Schrödinger maximal function on T1","authors":"Ciprian Demeter","doi":"10.1016/j.aim.2025.110186","DOIUrl":"10.1016/j.aim.2025.110186","url":null,"abstract":"<div><div>We prove (essentially) sharp <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>4</mn></mrow></msup></math></span> level set estimates for the periodic Schrödinger maximal operator in a certain range of the cut-off parameter.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"467 ","pages":"Article 110186"},"PeriodicalIF":1.5,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143510837","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Sequence entropy and IT-tuples for minimal group actions","authors":"Chunlin Liu , Xiangtong Wang , Leiye Xu","doi":"10.1016/j.aim.2025.110183","DOIUrl":"10.1016/j.aim.2025.110183","url":null,"abstract":"<div><div>Let <em>G</em> be an infinite discrete countable group and <span><math><mo>(</mo><mi>X</mi><mo>,</mo><mi>G</mi><mo>)</mo></math></span> a minimal <em>G</em>-system. First, we prove that<span><span><span><math><msubsup><mrow><mi>h</mi></mrow><mrow><mi>t</mi><mi>o</mi><mi>p</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup><mo>(</mo><mi>X</mi><mo>,</mo><mi>G</mi><mo>)</mo><mo>≥</mo><mi>log</mi><mo></mo><munder><mo>∑</mo><mrow><mi>μ</mi><mo>∈</mo><msup><mrow><mi>M</mi></mrow><mrow><mi>e</mi></mrow></msup><mo>(</mo><mi>X</mi><mo>,</mo><mi>G</mi><mo>)</mo></mrow></munder><msup><mrow><mi>e</mi></mrow><mrow><msubsup><mrow><mi>h</mi></mrow><mrow><mi>μ</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup><mo>(</mo><mi>X</mi><mo>,</mo><mi>G</mi><mo>)</mo></mrow></msup><mo>,</mo></math></span></span></span> where <span><math><msubsup><mrow><mi>h</mi></mrow><mrow><mi>t</mi><mi>o</mi><mi>p</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup><mo>(</mo><mi>X</mi><mo>,</mo><mi>G</mi><mo>)</mo></math></span> and <span><math><msubsup><mrow><mi>h</mi></mrow><mrow><mi>μ</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup><mo>(</mo><mi>X</mi><mo>,</mo><mi>G</mi><mo>)</mo></math></span> are the supremum of the topological and metric sequence entropy, respectively. Additionally, if <em>G</em> is abelian, there exists <span><math><mi>K</mi><mo>∈</mo><mi>N</mi><mo>∪</mo><mo>{</mo><mo>∞</mo><mo>}</mo></math></span> with <span><math><mi>log</mi><mo></mo><mi>K</mi><mo>≤</mo><msubsup><mrow><mi>h</mi></mrow><mrow><mi>t</mi><mi>o</mi><mi>p</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup><mo>(</mo><mi>X</mi><mo>,</mo><mi>G</mi><mo>)</mo></math></span> such that it is a regular <em>K</em>-to-one extension of its maximal equicontinuous factor.</div><div>Furthermore, for any infinite countable discrete group <em>G</em>, we show that if the factor map from a minimal <em>G</em>-system to its maximal equicontinuous factor is regular <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-to-one and almost <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-to-one, then the system admits <span><math><mo>⌈</mo><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>/</mo><msub><mrow><mi>K</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>⌉</mo></math></span>-IT-tuples, where <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>∈</mo><mi>N</mi><mo>∪</mo><mo>{</mo><mo>∞</mo><mo>}</mo></math></span> and <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>∈</mo><mi>N</mi></math></span>. As a corollary, we refine the upper bound on the number of ergodic measures for systems that are almost <em>N</em>-to-one extensions of their maximal equicontinuous factors and lack <em>K</em>-IT-tuples, thereby improving the result of Huang et al. (2021) <span><span>[17]</span></span>.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"467 ","pages":"Article 110183"},"PeriodicalIF":1.5,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143521276","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Superspace coinvariants and hyperplane arrangements","authors":"Robert Angarone , Patricia Commins , Trevor Karn , Satoshi Murai , Brendon Rhoades","doi":"10.1016/j.aim.2025.110185","DOIUrl":"10.1016/j.aim.2025.110185","url":null,"abstract":"<div><div>Let Ω be the <em>superspace ring</em> of polynomial-valued differential forms on affine <em>n</em>-space. The natural action of the symmetric group <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> on <em>n</em>-space induces an action of <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> on Ω. The <em>superspace coinvariant ring</em> is the quotient <em>SR</em> of Ω by the ideal generated by <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>-invariants with vanishing constant term. We give the first explicit basis of <em>SR</em>, proving a conjecture of Sagan and Swanson. Our techniques use the theory of hyperplane arrangements. We relate <em>SR</em> to instances of the Solomon–Terao algebras of Abe–Maeno–Murai–Numata and use exact sequences relating the derivation modules of certain ‘southwest closed’ arrangements to obtain the desired basis of <em>SR</em>.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"467 ","pages":"Article 110185"},"PeriodicalIF":1.5,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143521278","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Renaud Detcherry , Efstratia Kalfagianni , Adam S. Sikora
{"title":"Kauffman bracket skein modules of small 3-manifolds","authors":"Renaud Detcherry , Efstratia Kalfagianni , Adam S. Sikora","doi":"10.1016/j.aim.2025.110169","DOIUrl":"10.1016/j.aim.2025.110169","url":null,"abstract":"<div><div>The proof of Witten's finiteness conjecture established that the Kauffman bracket skein modules of closed 3-manifolds are finitely generated over <span><math><mi>Q</mi><mo>(</mo><mi>A</mi><mo>)</mo></math></span>. In this paper, we develop a novel method for computing these skein modules.</div><div>We show that if the skein module <span><math><mi>S</mi><mo>(</mo><mi>M</mi><mo>,</mo><mi>Q</mi><mo>[</mo><msup><mrow><mi>A</mi></mrow><mrow><mo>±</mo><mn>1</mn></mrow></msup><mo>]</mo><mo>)</mo></math></span> of <em>M</em> is tame (e.g. finitely generated over <span><math><mi>Q</mi><mo>[</mo><msup><mrow><mi>A</mi></mrow><mrow><mo>±</mo><mn>1</mn></mrow></msup><mo>]</mo></math></span>), and the <span><math><mi>S</mi><mi>L</mi><mo>(</mo><mn>2</mn><mo>,</mo><mi>C</mi><mo>)</mo></math></span>-character scheme is reduced, then the dimension <span><math><msub><mrow><mi>dim</mi></mrow><mrow><mi>Q</mi><mo>(</mo><mi>A</mi><mo>)</mo></mrow></msub><mo></mo><mspace></mspace><mi>S</mi><mo>(</mo><mi>M</mi><mo>,</mo><mi>Q</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo>)</mo></math></span> is the number of closed points in this character scheme. This, in particular, verifies a conjecture in the literature relating <span><math><msub><mrow><mi>dim</mi></mrow><mrow><mi>Q</mi><mo>(</mo><mi>A</mi><mo>)</mo></mrow></msub><mo></mo><mspace></mspace><mi>S</mi><mo>(</mo><mi>M</mi><mo>,</mo><mi>Q</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo>)</mo></math></span> to the Abouzaid-Manolescu <span><math><mi>S</mi><mi>L</mi><mo>(</mo><mn>2</mn><mo>,</mo><mi>C</mi><mo>)</mo></math></span>-Floer theoretic invariants, for infinite families of 3-manifolds.</div><div>We prove a criterion for reducedness of character varieties of closed 3-manifolds and use it to compute the skein modules of Dehn fillings of <span><math><mo>(</mo><mn>2</mn><mo>,</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></math></span>-torus knots and of the figure-eight knot. The later family gives the first instance of computations of skein modules for closed hyperbolic 3-manifolds.</div><div>We also prove that the skein modules of rational homology spheres have dimension at least 1 over <span><math><mi>Q</mi><mo>(</mo><mi>A</mi><mo>)</mo></math></span>.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"467 ","pages":"Article 110169"},"PeriodicalIF":1.5,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143521277","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
D. Cordero-Erausquin , N. Gozlan , S. Nakamura , H. Tsuji
{"title":"Duality and Heat flow","authors":"D. Cordero-Erausquin , N. Gozlan , S. Nakamura , H. Tsuji","doi":"10.1016/j.aim.2025.110161","DOIUrl":"10.1016/j.aim.2025.110161","url":null,"abstract":"<div><div>We reveal the relation between the Legendre transform of convex functions and Heat flow evolution, and how it applies to the functional Blaschke-Santaló inequality. We also describe local maximizers in this inequality.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"467 ","pages":"Article 110161"},"PeriodicalIF":1.5,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143510836","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Conformal product structures on compact Kähler manifolds","authors":"Andrei Moroianu , Mihaela Pilca","doi":"10.1016/j.aim.2025.110181","DOIUrl":"10.1016/j.aim.2025.110181","url":null,"abstract":"<div><div>A conformal product structure on a Riemannian manifold is a Weyl connection with reducible holonomy. We give the geometric description of all compact Kähler manifolds admitting conformal product structures.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"467 ","pages":"Article 110181"},"PeriodicalIF":1.5,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143510130","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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