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Simplicial intersection homology revisited 简单交同调的再探讨
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-01-16 DOI: 10.1016/j.topol.2025.109214
David Chataur , Martintxo Saralegi-Aranguren , Daniel Tanré
{"title":"Simplicial intersection homology revisited","authors":"David Chataur ,&nbsp;Martintxo Saralegi-Aranguren ,&nbsp;Daniel Tanré","doi":"10.1016/j.topol.2025.109214","DOIUrl":"10.1016/j.topol.2025.109214","url":null,"abstract":"<div><div>Intersection homology is defined for simplicial, singular and PL chains and it is well known that the three versions are isomorphic for a full filtered simplicial complex. In the literature, the isomorphism, between the singular and the simplicial situations of intersection homology, uses the PL case as an intermediate. Here we show directly that the canonical map between the simplicial and the singular intersection chains complexes is a quasi-isomorphism. This is similar to the classical proof for simplicial complexes, with an argument based on the concept of residual complex and not on skeletons.</div><div>This parallel between simplicial and singular approaches is also extended to the intersection blown-up cohomology that we introduced in a previous work. In the case of an orientable pseudomanifold, this cohomology owns a Poincaré isomorphism with the intersection homology, for any coefficient ring, thanks to a cap product with a fundamental class. So, the blown-up intersection cohomology of a pseudomanifold can be computed from a triangulation. Finally, we introduce a blown-up intersection cohomology for PL spaces and prove that it is isomorphic to the singular one.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"362 ","pages":"Article 109214"},"PeriodicalIF":0.6,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143134510","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
Divides with cusps and symmetric links 用尖头和对称链接划分
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-01-13 DOI: 10.1016/j.topol.2025.109207
Sakumi Sugawara
{"title":"Divides with cusps and symmetric links","authors":"Sakumi Sugawara","doi":"10.1016/j.topol.2025.109207","DOIUrl":"10.1016/j.topol.2025.109207","url":null,"abstract":"<div><div>A divide with cusps is the image of a proper generic immersion from finite intervals and circles into a 2-disk which allows to have cusps. A divide with cusps is a generalization of the notion of the divide which is introduced by A'Campo. From a divide with cusps, we can define the associated link in <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. In this paper, we give the characterization of links in <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> which can be described as the associated link of a divide with cusps. In particular, we prove that every strongly invertible link and 2-periodic link can be described as the link of a divide with cusps.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"362 ","pages":"Article 109207"},"PeriodicalIF":0.6,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143135532","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
On infinite-dimensional σ-homogeneous spaces 关于无穷维σ-齐次空间
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-01-09 DOI: 10.1016/j.topol.2025.109205
Jan van Mill , Roman Pol
{"title":"On infinite-dimensional σ-homogeneous spaces","authors":"Jan van Mill ,&nbsp;Roman Pol","doi":"10.1016/j.topol.2025.109205","DOIUrl":"10.1016/j.topol.2025.109205","url":null,"abstract":"<div><div>We prove that there is a continuum that is not the union of countably many homogeneous <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>δ</mi><mi>σ</mi></mrow></msub></math></span>-sets. We also make some remarks about coverings by strongly locally homogeneous subspaces.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"362 ","pages":"Article 109205"},"PeriodicalIF":0.6,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143134509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Singular braids, singular links and subgroups of camomile type 甘菊型的奇异辫状、奇异链和子群
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-01-09 DOI: 10.1016/j.topol.2025.109206
Valeriy G. Bardakov , Tatyana A. Kozlovskaya
{"title":"Singular braids, singular links and subgroups of camomile type","authors":"Valeriy G. Bardakov ,&nbsp;Tatyana A. Kozlovskaya","doi":"10.1016/j.topol.2025.109206","DOIUrl":"10.1016/j.topol.2025.109206","url":null,"abstract":"<div><div>In this paper we find a finite set of generators and defining relations for the singular pure braid group <span><math><mi>S</mi><msub><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>, <span><math><mi>n</mi><mo>≥</mo><mn>3</mn></math></span>, that is a subgroup of the singular braid group <span><math><mi>S</mi><msub><mrow><mi>B</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>. Using this presentation, we prove that the center of <span><math><mi>S</mi><msub><mrow><mi>B</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> (which is equal to the center of <span><math><mi>S</mi><msub><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> for <span><math><mi>n</mi><mo>≥</mo><mn>3</mn></math></span>) is a direct factor in <span><math><mi>S</mi><msub><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> but it is not a direct factor in <span><math><mi>S</mi><msub><mrow><mi>B</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>. We introduce subgroups of camomile type and prove that the singular pure braid group <span><math><mi>S</mi><msub><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>, <span><math><mi>n</mi><mo>≥</mo><mn>5</mn></math></span>, is a subgroup of camomile type in <span><math><mi>S</mi><msub><mrow><mi>B</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>. Also we construct the fundamental singquandle using a representation of the singular braid monoid by endomorphisms of free quandle. For any singular link we define some family of groups which are invariants of this link.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"362 ","pages":"Article 109206"},"PeriodicalIF":0.6,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143135530","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
Some properties of pre-topological groups 前拓扑群的一些性质
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-01-08 DOI: 10.1016/j.topol.2025.109204
Fucai Lin , Ting Wu , Yufan Xie , Meng Bao
{"title":"Some properties of pre-topological groups","authors":"Fucai Lin ,&nbsp;Ting Wu ,&nbsp;Yufan Xie ,&nbsp;Meng Bao","doi":"10.1016/j.topol.2025.109204","DOIUrl":"10.1016/j.topol.2025.109204","url":null,"abstract":"<div><div>In this paper, the concepts of pre-topological groups and some generalizations of pre-topological groups are posed. First, some basic properties of pre-topological groups are systematically investigated; in particular, we prove that each <span><math><msub><mrow><mi>T</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> pre-topological group is regular, and every <span><math><msub><mrow><mi>T</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> almost topological group is completely regular which extends A.A. Markov's theorem to the class of almost topological groups. Moreover, it is shown that an almost topological group is <em>τ</em>-narrow if and only if it can be embedded as a subgroup of a pre-topological <em>C</em>-product of almost topological groups of weight less than or equal to <em>τ</em>. Finally, the cardinal invariant, the precompactness and the resolvability are investigated in the class of pre-topological groups.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"362 ","pages":"Article 109204"},"PeriodicalIF":0.6,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143135536","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
Verbal quandles with one parameter 只有一个参数
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-01-07 DOI: 10.1016/j.topol.2025.109203
Elizaveta Markhinina , Timur Nasybullov
{"title":"Verbal quandles with one parameter","authors":"Elizaveta Markhinina ,&nbsp;Timur Nasybullov","doi":"10.1016/j.topol.2025.109203","DOIUrl":"10.1016/j.topol.2025.109203","url":null,"abstract":"<div><div>We find all words <span><math><mi>W</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>)</mo></math></span> in the free group <span><math><mi>F</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>)</mo></math></span>, such that for every group <em>G</em> and element <span><math><mi>c</mi><mo>∈</mo><mi>G</mi></math></span> the algebraic system <span><math><mo>(</mo><mi>G</mi><mo>,</mo><msub><mrow><mo>⁎</mo></mrow><mrow><mi>W</mi><mo>,</mo><mi>c</mi></mrow></msub><mo>)</mo></math></span> with the binary operation <span><math><msub><mrow><mo>⁎</mo></mrow><mrow><mi>W</mi><mo>,</mo><mi>c</mi></mrow></msub></math></span> given by <span><math><mi>a</mi><msub><mrow><mo>⁎</mo></mrow><mrow><mi>W</mi><mo>,</mo><mi>c</mi></mrow></msub><mi>b</mi><mo>=</mo><mi>W</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></span> for <span><math><mi>a</mi><mo>,</mo><mi>b</mi><mo>∈</mo><mi>G</mi></math></span> is a quandle. Such quandles are called verbal quandles with one parameter.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"362 ","pages":"Article 109203"},"PeriodicalIF":0.6,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143135534","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
Strongly topological gyrogroups with generalized countably compact properties 具有广义可数紧性的强拓扑陀螺群
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-01-03 DOI: 10.1016/j.topol.2024.109202
Jing Zhang, Kaixiong Lin
{"title":"Strongly topological gyrogroups with generalized countably compact properties","authors":"Jing Zhang,&nbsp;Kaixiong Lin","doi":"10.1016/j.topol.2024.109202","DOIUrl":"10.1016/j.topol.2024.109202","url":null,"abstract":"<div><div>In this note, some characterizations of strongly topological gyrogroups are given. It is proved that: (1) a strongly topological gyrogroup <em>G</em> has a <em>q</em>-point iff it is a quasi-perfect preimage of some metrizable space; (2) a strongly topological gyrogroup <em>G</em> has a strict <em>q</em>-point iff it is a sequential-perfect preimage of some metrizable space; (3) a strongly topological gyrogroup <em>G</em> contains a strong <em>q</em>-point iff it is a strongly sequential-perfect preimage of some metrizable space; (4) a strongly topological gyrocommutative gyrogroup <em>G</em> contains a pseudocompactness point iff there exists a continuous open mapping <em>f</em> from <em>G</em> onto a metrizable space <em>M</em> such that <span><math><msup><mrow><mi>f</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>(</mo><mi>F</mi><mo>)</mo></math></span> is an <em>r</em>-pseudocompact set in <em>G</em> for each <em>r</em>-pseudocompact set <em>F</em> in <em>M</em>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"361 ","pages":"Article 109202"},"PeriodicalIF":0.6,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143147419","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
Expansive actions and the GCH 扩张行动和GCH
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-01-02 DOI: 10.1016/j.topol.2024.109190
Luis Ferrari
{"title":"Expansive actions and the GCH","authors":"Luis Ferrari","doi":"10.1016/j.topol.2024.109190","DOIUrl":"10.1016/j.topol.2024.109190","url":null,"abstract":"<div><div>In this paper, we provide a generalization in terms of actions of the theorem 2.2 in <span><span>[7]</span></span> establishing a necessary and sufficient condition for the existence of expansive homeomorphisms on countable compact spaces. The study of the cardinalities of groups acting expansively will lead us to a relationship between expansivity and the Generalized Continuum Hypothesis.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"361 ","pages":"Article 109190"},"PeriodicalIF":0.6,"publicationDate":"2025-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143147015","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
The Bowen-Franks type theorems for multivalued maps and impulsive differential equations 多值映射和脉冲微分方程的Bowen-Franks型定理
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-01-01 DOI: 10.1016/j.topol.2024.109080
Jan Andres, Pavel Ludvík
{"title":"The Bowen-Franks type theorems for multivalued maps and impulsive differential equations","authors":"Jan Andres,&nbsp;Pavel Ludvík","doi":"10.1016/j.topol.2024.109080","DOIUrl":"10.1016/j.topol.2024.109080","url":null,"abstract":"<div><div>The aim of the present paper is to extend the well known Bowen-Franks type theorems to interval and circle multivalued maps. In this way, a positive topological entropy, including its lower estimate, can be implied by the existence of periodic orbits whose orders differ from a power of 2, or provided the topological degree of given circle maps is absolutely greater than 1. Simple applications are also given to impulsive differential equations.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"359 ","pages":"Article 109080"},"PeriodicalIF":0.6,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143156706","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
R∞-property for finitely generated torsion-free 2-step nilpotent groups of small Hirsch length 小Hirsch长度有限生成无扭转2步幂零群的R∞性质
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-01-01 DOI: 10.1016/j.topol.2024.109084
Karel Dekimpe , Maarten Lathouwers
{"title":"R∞-property for finitely generated torsion-free 2-step nilpotent groups of small Hirsch length","authors":"Karel Dekimpe ,&nbsp;Maarten Lathouwers","doi":"10.1016/j.topol.2024.109084","DOIUrl":"10.1016/j.topol.2024.109084","url":null,"abstract":"<div><div>In this paper we will show that finitely generated torsion-free 2-step nilpotent groups of Hirsch length at most 6 do not have the <span><math><msub><mrow><mi>R</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span>-property, while there are examples of such groups of Hirsch length 7 that do have the <span><math><msub><mrow><mi>R</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span>-property.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"359 ","pages":"Article 109084"},"PeriodicalIF":0.6,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143156707","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
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