Advances in Mathematics最新文献

{"title":"An atomic Coxeter presentation","authors":"Hankyung Ko","doi":"10.1016/j.aim.2025.110252","DOIUrl":"10.1016/j.aim.2025.110252","url":null,"abstract":"<div><div>We study parabolic double cosets in a Coxeter system by decomposing them into atom(ic coset)s, a generalization of simple reflections introduced in a joint work with Elias, Libedinsky, Patimo. We define and classify braid relations between compositions of atoms and prove a Matsumoto theorem. Together with a quadratic relation, our braid relations give a presentation of nilCoxeter algebroids similar to Demazure's presentation of nilCoxeter algebras. Our consideration of reduced compositions of atoms gives rise to a new combinatorial structure, which is equipped with a length function and a Bruhat order and is realized as Tits cone intersections in the sense of Iyama-Wemyss.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"470 ","pages":"Article 110252"},"PeriodicalIF":1.5,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759213","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":"Topology and approximation of weak G-bundles in the supercritical dimensions","authors":"Swarnendu Sil","doi":"10.1016/j.aim.2025.110229","DOIUrl":"10.1016/j.aim.2025.110229","url":null,"abstract":"<div><div>For analyzing stationary Yang-Mills connections in higher dimensions, one has to work with Morrey-Sobolev bundles and connections. The transition maps for a Morrey-Sobolev principal <em>G</em>-bundles are not continuous and thus the usual notion of topology does not make sense. In this work, we develop the notion of a topological isomorphism class for a bundle-connection pair <span><math><mo>(</mo><mi>P</mi><mo>,</mo><mi>A</mi><mo>)</mo></math></span> and use these notions to derive several approximability results for bundles and connections in the Morrey-Sobolev setting. Our proofs follow a connection-oriented approach and also highlight the fact that in the low regularity regime, the regularity of the bundle and connection are intertwined. Our results parallel the theory of the topological degree and approximation results for manifold-valued VMO maps.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"470 ","pages":"Article 110229"},"PeriodicalIF":1.5,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759211","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":"Hyperbolic distortion and conformality at the boundary","authors":"Pavel Gumenyuk ,&nbsp;Maria Kourou ,&nbsp;Annika Moucha ,&nbsp;Oliver Roth","doi":"10.1016/j.aim.2025.110251","DOIUrl":"10.1016/j.aim.2025.110251","url":null,"abstract":"<div><div>We characterize two classical types of conformality of a holomorphic self-map of the unit disk at a boundary point — the existence of a finite angular derivative in the sense of Carathéodory and the weaker property of angle preservation — in terms of the non-tangential asymptotic behavior of the hyperbolic distortion of the map. We also provide an operator-theoretic characterization of the existence of a finite angular derivative based on Hilbert space methods. As an application we study the backward dynamics of discrete dynamical systems induced by holomorphic self-maps, and characterize the regularity of the associated pre-models in terms of a Blaschke-type condition involving the hyperbolic distortion along regular backward orbits.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"470 ","pages":"Article 110251"},"PeriodicalIF":1.5,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759381","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":"Taut foliations, braid positivity, and unknot detection","authors":"Siddhi Krishna","doi":"10.1016/j.aim.2025.110233","DOIUrl":"10.1016/j.aim.2025.110233","url":null,"abstract":"<div><div>We study <em>positive braid knots</em> (the knots in the three–sphere realized as positive braid closures) through the lens of the L-space conjecture. This conjecture predicts that if <em>K</em> is a non-trivial positive braid knot, then for all <span><math><mi>r</mi><mo>&lt;</mo><mn>2</mn><mi>g</mi><mo>(</mo><mi>K</mi><mo>)</mo><mo>−</mo><mn>1</mn></math></span>, the 3-manifold obtained via <em>r</em>-framed Dehn surgery along <em>K</em> admits a taut foliation. Our main result provides some positive evidence towards this conjecture: we construct taut foliations in such manifolds whenever <span><math><mi>r</mi><mo>&lt;</mo><mi>g</mi><mo>(</mo><mi>K</mi><mo>)</mo><mo>+</mo><mn>1</mn></math></span>. As an application, we produce a novel braid positivity obstruction for cable knots by proving that <em>the</em> <span><math><mo>(</mo><mi>n</mi><mo>,</mo><mo>±</mo><mn>1</mn><mo>)</mo></math></span><em>–cable of a knot K is braid positive if and only if K is the unknot</em>. We also present some curious examples demonstrating the limitations of our construction; these examples can also be viewed as providing some negative evidence towards the L-space conjecture. Finally, we apply our main result to produce taut foliations in some splicings of knot exteriors.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"470 ","pages":"Article 110233"},"PeriodicalIF":1.5,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759383","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":"Embedding spaces of split links","authors":"Rachael Boyd ,&nbsp;Corey Bregman","doi":"10.1016/j.aim.2025.110235","DOIUrl":"10.1016/j.aim.2025.110235","url":null,"abstract":"<div><div>We study the homotopy type of the space <span><math><mi>E</mi><mo>(</mo><mi>L</mi><mo>)</mo></math></span> of unparametrised embeddings of a split link <span><math><mi>L</mi><mo>=</mo><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>⊔</mo><mo>…</mo><mo>⊔</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. Our main result is a simple description of the fundamental group, or motion group, of <span><math><mi>E</mi><mo>(</mo><mi>L</mi><mo>)</mo></math></span>, and we extend this to a description of the motion group of embeddings in <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. The main tool we build is a semi-simplicial space of separating systems, which we show is homotopy equivalent to <span><math><mi>E</mi><mo>(</mo><mi>L</mi><mo>)</mo></math></span>. This combinatorial object provides a gateway to studying the homotopy type of <span><math><mi>E</mi><mo>(</mo><mi>L</mi><mo>)</mo></math></span> via the homotopy type of the spaces <span><math><mi>E</mi><mo>(</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>)</mo></math></span>.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"470 ","pages":"Article 110235"},"PeriodicalIF":1.5,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759384","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":"Torus knotted Reeb dynamics and the Calabi invariant","authors":"Jo Nelson ,&nbsp;Morgan Weiler","doi":"10.1016/j.aim.2025.110236","DOIUrl":"10.1016/j.aim.2025.110236","url":null,"abstract":"<div><div>We establish quantitative existence, action, and linking bounds for all Reeb orbits associated to any contact form on the standard tight three-sphere admitting the standard transverse positive <span><math><mi>T</mi><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></span> torus knot as an elliptic Reeb orbit with canonically determined rotation numbers. This can be interpreted through an ergodic lens for Reeb flows transverse to a surface of section. Our results also allow us to deduce an upper bound on the mean action of periodic orbits of naturally associated classes of area preserving diffeomorphisms of the associated Seifert surfaces of genus <span><math><mo>(</mo><mi>p</mi><mo>−</mo><mn>1</mn><mo>)</mo><mo>(</mo><mi>q</mi><mo>−</mo><mn>1</mn><mo>)</mo><mo>/</mo><mn>2</mn></math></span> in terms of the Calabi invariant, without the need for genericity or Hamiltonian hypotheses. Our proofs utilize knot filtered embedded contact homology, which was first introduced and computed by Hutchings for the standard transverse unknot in the irrational ellipsoids and further developed in our previous work. We continue our development of nontoric methods for embedded contact homology and establish the knot filtration on the embedded contact homology chain complex of the standard tight three-sphere with respect to positive <span><math><mi>T</mi><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></span> torus knots, where there are nonvanishing differentials. We also obtain obstructions to the existence of exact symplectic cobordisms between positive transverse torus knots.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"470 ","pages":"Article 110236"},"PeriodicalIF":1.5,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759212","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":"Kähler gradient Ricci solitons with large symmetry","authors":"Hung Tran","doi":"10.1016/j.aim.2025.110253","DOIUrl":"10.1016/j.aim.2025.110253","url":null,"abstract":"<div><div>Let <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo>,</mo><mi>J</mi><mo>,</mo><mi>f</mi><mo>)</mo></math></span> be an irreducible non-trivial Kähler gradient Ricci soliton of real dimension 2<em>n</em>. We show that its group of isometries is of dimension at most <span><math><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and the case of equality is characterized. As a consequence, our framework shows the uniqueness of <span><math><mi>U</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span>-invariant Kähler gradient Ricci solitons constructed earlier. There are corollaries regarding the groups of automorphisms or affine transformations and a general version for almost Hermitian GRS. The approach is based on a connection to the geometry of an almost contact metric structure.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"470 ","pages":"Article 110253"},"PeriodicalIF":1.5,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759380","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":"Cauchy convergence in V-normed categories","authors":"Maria Manuel Clementino ,&nbsp;Dirk Hofmann ,&nbsp;Walter Tholen","doi":"10.1016/j.aim.2025.110247","DOIUrl":"10.1016/j.aim.2025.110247","url":null,"abstract":"<div><div>Building on the notion of normed category as suggested by Lawvere, we introduce notions of Cauchy convergence and cocompleteness for such categories that differ from proposals in previous works. Key to our approach is to treat them consequentially as categories enriched in the monoidal-closed category of normed sets, <em>i.e.</em>, of sets which come with a norm function. Our notions lead to the anticipated outcomes for individual metric spaces or the additive groups of normed vector spaces considered as small normed categories. But they quickly become more challenging when we consider large categories, such as the categories of all semi-normed or normed vector spaces and all linear maps as morphisms, not just because norms of vectors need to be allowed to have value ∞ in order to guarantee the existence of colimits of (sufficiently many) infinite sequences. These categories, along with categories of generalized metric spaces, are the key example categories discussed in detail in this paper.</div><div>Working with a general commutative quantale <span><math><mi>V</mi></math></span> as a value recipient for norms, rather than only with Lawvere's quantale <span><math><msub><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msub></math></span> of the extended real half-line, we observe that the categorically atypical, and perhaps even irritating, structure gap between objects and morphisms in the example categories is already present in the underlying normed category of the enriching category of <span><math><mi>V</mi></math></span>-normed sets. To show that the normed category and, in fact, all presheaf categories over it, are Cauchy cocomplete, we assume the quantale <span><math><mi>V</mi></math></span> to satisfy a couple of light alternative extra properties which, however, are satisfied in all instances of interest to us. Of utmost importance to the general theory is the fact that our notion of Cauchy convergence is subsumed by the notion of weighted colimit of enriched category theory. With this theory and, in particular, with results of Albert, Kelly and Schmitt, we are able to prove that all <span><math><mi>V</mi></math></span>-normed categories have correct-size Cauchy cocompletions, for <span><math><mi>V</mi></math></span> satisfying our light alternative assumptions.</div><div>We also show that our notions are suitable to prove a Banach Fixed Point Theorem for contractive endofunctors of Cauchy cocomplete normed categories.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"470 ","pages":"Article 110247"},"PeriodicalIF":1.5,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759382","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":"Exact values of generic subrank","authors":"Paweł Pielasa ,&nbsp;Matouš Šafránek ,&nbsp;Anatoli Shatsila","doi":"10.1016/j.aim.2025.110234","DOIUrl":"10.1016/j.aim.2025.110234","url":null,"abstract":"<div><div>In this article we prove the subrank of a generic tensor in <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>n</mi><mo>,</mo><mi>n</mi><mo>,</mo><mi>n</mi></mrow></msup></math></span> to be <span><math><mi>Q</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mo>⌊</mo><msqrt><mrow><mn>3</mn><mi>n</mi><mo>−</mo><mn>2</mn></mrow></msqrt><mo>⌋</mo></math></span> by providing a lower bound to the known upper bound. More generally, we find the generic subrank of tensors of all orders and dimensions. This answers two open questions posed in <span><span>[5]</span></span>. Finally, we compute dimensions of varieties of tensors of subrank at least <em>r</em>.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"469 ","pages":"Article 110234"},"PeriodicalIF":1.5,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143746366","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":"Equivariant birational geometry of cubic fourfolds and derived categories","authors":"Christian Böhning ,&nbsp;Hans-Christian Graf von Bothmer ,&nbsp;Yuri Tschinkel","doi":"10.1016/j.aim.2025.110249","DOIUrl":"10.1016/j.aim.2025.110249","url":null,"abstract":"<div><div>We study equivariant birationality from the perspective of derived categories. We produce examples of nonlinearizable but stably linearizable actions of finite groups on smooth cubic fourfolds.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"469 ","pages":"Article 110249"},"PeriodicalIF":1.5,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143746669","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}