Advances in Mathematics最新文献

Dynamics of weighted shifts on ℓp-sums and c0-sums

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-04-05 DOI: 10.1016/j.aim.2025.110250

Quentin Menet , Dimitris Papathanasiou

引用次数: 0

Diophantine approximation and the Mass Transference Principle: Incorporating the unbounded setup

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-04-04 DOI: 10.1016/j.aim.2025.110248

Bing Li , Lingmin Liao , Sanju Velani , Baowei Wang , Evgeniy Zorin

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An atomic Coxeter presentation 原子考斯特演示

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-04-03 DOI: 10.1016/j.aim.2025.110252

Hankyung Ko

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Topology and approximation of weak G-bundles in the supercritical dimensions 超临界维度中弱 G 束的拓扑与近似

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-04-03 DOI: 10.1016/j.aim.2025.110229

Swarnendu Sil

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Hyperbolic distortion and conformality at the boundary

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-04-03 DOI: 10.1016/j.aim.2025.110251

Pavel Gumenyuk , Maria Kourou , Annika Moucha , Oliver Roth

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Taut foliations, braid positivity, and unknot detection

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-04-03 DOI: 10.1016/j.aim.2025.110233

Siddhi Krishna

{"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><</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><</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}

引用次数: 0

Embedding spaces of split links

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-04-03 DOI: 10.1016/j.aim.2025.110235

Rachael Boyd , Corey Bregman

引用次数: 0

Kähler gradient Ricci solitons with large symmetry

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-04-03 DOI: 10.1016/j.aim.2025.110253

Hung Tran

引用次数: 0

Cauchy convergence in V-normed categories

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-04-03 DOI: 10.1016/j.aim.2025.110247

Maria Manuel Clementino , Dirk Hofmann , Walter Tholen

{"title":"Cauchy convergence in V-normed categories","authors":"Maria Manuel Clementino , Dirk Hofmann , 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}

引用次数: 0

Torus knotted Reeb dynamics and the Calabi invariant 环结里布动力学和卡拉比不变量

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-04-03 DOI: 10.1016/j.aim.2025.110236

Jo Nelson , Morgan Weiler

{"title":"Torus knotted Reeb dynamics and the Calabi invariant","authors":"Jo Nelson , 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}

引用次数: 0