Topology and its Applications最新文献_第4页

On isometric universality of spaces of metrics 论度量空间的等距普适性

IF 0.6 4区数学

Topology and its Applications Pub Date : 2025-04-17 DOI: 10.1016/j.topol.2025.109394

Yoshito Ishiki , Katsuhisa Koshino

引用次数: 0

Bar-Natan theory and tunneling between incompressible surfaces in 3-manifolds Bar-Natan理论与3流形中不可压缩表面间的隧穿

IF 0.6 4区数学

Topology and its Applications Pub Date : 2025-04-16 DOI: 10.1016/j.topol.2025.109390

Uwe Kaiser

{"title":"Bar-Natan theory and tunneling between incompressible surfaces in 3-manifolds","authors":"Uwe Kaiser","doi":"10.1016/j.topol.2025.109390","DOIUrl":"10.1016/j.topol.2025.109390","url":null,"abstract":"<div><div>In [16] the author defined for each commutative Frobenius algebra a skein module of surfaces in a 3-manifold M bounding a closed 1-manifold <math><mi>α</mi><mo>⊂</mo><mo>∂</mo><mi>M</mi></math>. The surface components are colored by elements of the Frobenius algebra. The modules are called the Bar-Natan modules of <math><mo>(</mo><mi>M</mi><mo>,</mo><mi>α</mi><mo>)</mo></math>. In this article we show that Bar-Natan modules are colimit modules of functors associated to Frobenius algebras, decoupling topology from algebra. The functors are defined on a category of 3-dimensional compression bordisms embedded in cylinders over M and take values in a linear category defined from the Frobenius algebra. The relation with the <math><mn>1</mn><mo>+</mo><mn>1</mn></math>-dimensional topological quantum field theory functor associated to the Frobenius algebra is studied. We show that the geometric content of the skein modules is contained in a tunneling graph of <math><mo>(</mo><mi>M</mi><mo>,</mo><mi>α</mi><mo>)</mo></math>, providing a natural presentation of the Bar-Natan module by application of the functor defined from the algebra. Such presentations have essentially been stated in [16] and [2] using ad-hoc arguments. But they appear naturally on the background of the Bar-Natan functor and associated categorical considerations. We discuss in general how to deduce presentations of colimit modules for functors into module categories in terms of minimal terminal sets of objects of the category in the categorical setting. We also sketch the construction of a bicategory version of the Bar-Natan functor.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"369 ","pages":"Article 109390"},"PeriodicalIF":0.6,"publicationDate":"2025-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143863529","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

An answer to a problem on topologies of function spaces on metric measure spaces 度量度量空间上函数空间拓扑问题的解答

IF 0.6 4区数学

Topology and its Applications Pub Date : 2025-04-16 DOI: 10.1016/j.topol.2025.109391

Hanbiao Yang , Kaihong Dong , Yingying Jin

{"title":"An answer to a problem on topologies of function spaces on metric measure spaces","authors":"Hanbiao Yang , Kaihong Dong , Yingying Jin","doi":"10.1016/j.topol.2025.109391","DOIUrl":"10.1016/j.topol.2025.109391","url":null,"abstract":"<div><div>Let X be a metric measure space. In the paper K. Koshino (2020) [6], it was proved that if X satisfies some conditions, then the <math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math>-space <math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>X</mi><mo>)</mo></math> on X is homeomorphic to the product space s of countably infinitely many open intervals <math><mo>(</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math>, and the subspace <math><msub><mrow><mi>C</mi></mrow><mrow><mi>u</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math> of <math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>X</mi><mo>)</mo></math> consisting of uniformly continuous maps is also homeomorphic to the subspace <math><msub><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msub></math> of s consisting of sequences converging to 0. Then it was asked whether or not the pair <math><mo>(</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>X</mi><mo>)</mo><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>u</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo><mo>)</mo></math> is homeomorphic to <math><mo>(</mo><mi>s</mi><mo>,</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></math>. In this note, we will present some examples of metric measure spaces X in the both cases where those pairs are homeomorphic and not, and show that they are not homeomorphic if X is a Euclidean space or its cube with the usual metric and the Lebesgue measure.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"370 ","pages":"Article 109391"},"PeriodicalIF":0.6,"publicationDate":"2025-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143903973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Induced mappings on Pixley-Roy hyperspace Pixley-Roy超空间上的诱导映射

IF 0.6 4区数学

Topology and its Applications Pub Date : 2025-04-10 DOI: 10.1016/j.topol.2025.109389

Enrique Castañeda-Alvarado, David Maya, Miguel Angel Morales-Bautista, Fernando Orozco-Zitli

引用次数: 0

Normal forms for rational 3-tangles 有理3-缠结的正规形式

IF 0.6 4区数学

Topology and its Applications Pub Date : 2025-04-08 DOI: 10.1016/j.topol.2025.109388

Bo-hyun Kwon , Jung Hoon Lee

引用次数: 0

Differential forms on diffeological spaces and diffeological gluing, I 微分形式的微分空间和微分胶合，1

IF 0.6 4区数学

Topology and its Applications Pub Date : 2025-04-07 DOI: 10.1016/j.topol.2025.109387

Ekaterina Pervova

引用次数: 0

Furstenberg type theorems for strongly transitive maps 强传递映射的Furstenberg型定理

IF 0.6 4区数学

Topology and its Applications Pub Date : 2025-04-07 DOI: 10.1016/j.topol.2025.109386

Francisco Antonio-Balderas , Leobardo Fernández , José Jirash , Jorge Moreno-Montes , Leonel Rito

{"title":"Furstenberg type theorems for strongly transitive maps","authors":"Francisco Antonio-Balderas , Leobardo Fernández , José Jirash , Jorge Moreno-Montes , Leonel Rito","doi":"10.1016/j.topol.2025.109386","DOIUrl":"10.1016/j.topol.2025.109386","url":null,"abstract":"<div><div>Given a dynamical system <math><mo>(</mo><mi>X</mi><mo>,</mo><mi>f</mi><mo>)</mo></math> and a positive integer n, we study the concept of strong transitivity in the induced map <math><msup><mrow><mi>f</mi></mrow><mrow><mo>×</mo><mi>n</mi></mrow></msup><mo>:</mo><msup><mrow><mi>X</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>→</mo><msup><mrow><mi>X</mi></mrow><mrow><mi>n</mi></mrow></msup></math>. The main problem is to figure out when the strong transitivity of <math><msup><mrow><mi>f</mi></mrow><mrow><mo>×</mo><mn>2</mn></mrow></msup></math> implies the strong transitivity of <math><msup><mrow><mi>f</mi></mrow><mrow><mo>×</mo><mi>n</mi></mrow></msup></math>. In certain spaces, such as finite connected graphs, we show that if <math><msup><mrow><mi>f</mi></mrow><mrow><mo>×</mo><mn>2</mn></mrow></msup></math> is strongly transitive then f is strongly mixing which also implies that <math><msup><mrow><mi>f</mi></mrow><mrow><mo>×</mo><mi>n</mi></mrow></msup></math> is strongly transitive for any n. We also give an example of a map <math><mi>f</mi><mo>:</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>→</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msup></math> which is strongly mixing but not exact, showing that our result is optimal in finite graphs.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"369 ","pages":"Article 109386"},"PeriodicalIF":0.6,"publicationDate":"2025-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143815222","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

A homotopy approach for maps with a continuous inclusion property 具有连续包含性质映射的同伦方法

IF 0.6 4区数学

Topology and its Applications Pub Date : 2025-04-04 DOI: 10.1016/j.topol.2025.109384

Donal O'Regan

引用次数: 0

The trunk number of satellite knots and Thurston norm 卫星节和瑟斯顿规范的主干数

IF 0.6 4区数学

Topology and its Applications Pub Date : 2025-04-03 DOI: 10.1016/j.topol.2025.109383

Zehan Pan

引用次数: 0

Isometries of spaces of compact convex subsets of Busemann spaces Busemann空间的紧凸子集空间的等距