Topology and its Applications最新文献

{"title":"Cohomology rings of oriented Grassmann manifolds G˜2t,4","authors":"Uroš A. Colović,&nbsp;Milica Jovanović ,&nbsp;Branislav I. Prvulović","doi":"10.1016/j.topol.2025.109318","DOIUrl":"10.1016/j.topol.2025.109318","url":null,"abstract":"<div><div>We give a description of the mod 2 cohomology algebra of the oriented Grassmann manifold <span><math><msub><mrow><mover><mrow><mi>G</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mi>t</mi></mrow></msup><mo>,</mo><mn>4</mn></mrow></msub></math></span> as the quotient of a polynomial algebra by a certain ideal. In the process we find a Gröbner basis for that ideal, which we then use to exhibit an additive basis for <span><math><msup><mrow><mi>H</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><msub><mrow><mover><mrow><mi>G</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mi>t</mi></mrow></msup><mo>,</mo><mn>4</mn></mrow></msub><mo>;</mo><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math></span>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"367 ","pages":"Article 109318"},"PeriodicalIF":0.6,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143549665","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}

{"title":"Properties of equi-Baire 1 and equi-Lebesgue families of functions","authors":"Marek Balcerzak ,&nbsp;Ľubica Holá ,&nbsp;Dušan Holý","doi":"10.1016/j.topol.2025.109317","DOIUrl":"10.1016/j.topol.2025.109317","url":null,"abstract":"<div><div>We study several properties of equi-Baire 1 families of functions between metric spaces. We consider the related equi-Lebesgue property for such families. We examine the behavior of equi-Baire 1 and equi-Lebesgue families with respect to pointwise and uniform convergence. In particular, we obtain a criterion for a choice of a uniformly convergent subsequence from a sequence of functions that form an equi-Baire 1 family, which solves a problem posed in <span><span>[3]</span></span>. Finally, we discuss the notion of equi-cliquishness and relations between equi-Baire 1 families and sets of equi-continuity points.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"367 ","pages":"Article 109317"},"PeriodicalIF":0.6,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143561854","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}

{"title":"Handle numbers of guts of sutured manifolds and nearly fibered knots","authors":"Kenneth L. Baker ,&nbsp;Fabiola Manjarrez-Gutiérrez","doi":"10.1016/j.topol.2025.109316","DOIUrl":"10.1016/j.topol.2025.109316","url":null,"abstract":"<div><div>Extending Haken's Theorem to product annuli and disks for Heegaard splittings of sutured manifolds, we show that the handle number of an irreducible sutured manifold equals the handle number of its guts. We further show that reduced sutured manifolds with torus boundary contained in <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> fall in to three types that generalize the three models of guts of knots that are nearly fibered in the instanton or Heegaard Floer sense. In conjunction with these results and another concerning uniqueness of incompressible Seifert surfaces, we show that while many nearly fibered knots have handle number 2 and a unique incompressible Seifert surface, some have handle number 4 and others have extra incompressible Seifert surfaces. Examples of nearly fibered knots with non-isotopic incompressible Seifert surfaces are exhibited.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"367 ","pages":"Article 109316"},"PeriodicalIF":0.6,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143561855","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}

{"title":"Shore sets in a dendroid and Jones' function T","authors":"Alejandro Illanes ,&nbsp;Rocío Leonel ,&nbsp;Verónica Martínez-de-la-Vega","doi":"10.1016/j.topol.2025.109315","DOIUrl":"10.1016/j.topol.2025.109315","url":null,"abstract":"<div><div>We study the behavior of <span><math><mi>T</mi><mo>(</mo><mi>A</mi><mo>)</mo></math></span>, where <em>T</em> is the Jones' function and <em>A</em> is a closed shore set in a dendroid <em>X</em>. We show an example of a smooth dendroid <em>X</em> and a shore subcontinuum <em>A</em> of <em>X</em> such that <span><math><mi>T</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo>=</mo><mi>X</mi></math></span>. On the other extreme, we prove that if <em>X</em> is a fan (a dendroid with exactly one ramification point), then for each closed shore subset <em>A</em> of <em>X</em>, <span><math><msub><mrow><mi>int</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>(</mo><mi>T</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo>)</mo><mo>=</mo><mo>∅</mo></math></span>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"367 ","pages":"Article 109315"},"PeriodicalIF":0.6,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143600786","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}

{"title":"Infinite families of standard Cappell-Shaneson homotopy 4-spheres","authors":"Kazunori Iwaki","doi":"10.1016/j.topol.2025.109293","DOIUrl":"10.1016/j.topol.2025.109293","url":null,"abstract":"<div><div>Cappell-Shaneson homotopy 4-spheres (CS spheres) are potential counterexamples of the smooth 4-dimensional Poincaré conjecture. The simplest CS spheres was proven to be diffeomorphic to the standard 4-sphere in 2010. Another family of CS spheres was proven to be diffeomorphic to the standard 4-sphere in 2023. In this paper, we prove more CS spheres are standard. We give 145 new infinite families of CS spheres which are diffeomorphic to the standard 4-sphere.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"366 ","pages":"Article 109293"},"PeriodicalIF":0.6,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143529235","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}

{"title":"Function spaces of Lawson-compact algebraic domains","authors":"Wei Luan ,&nbsp;Qingguo Li","doi":"10.1016/j.topol.2025.109295","DOIUrl":"10.1016/j.topol.2025.109295","url":null,"abstract":"<div><div>In this paper, we investigate function spaces of Lawson-compact algebraic domains. It is proved that a dcpo is a Lawson-compact algebraic domain iff there is an approximate identity consisting of Scott-continuous kernel operators whose images are prefinite algebraic domains. Using this fact, we obtain the following results:<ul><li><span>(1)</span><span><div>The function space from a bifinite domain to a Lawson-compact algebraic domain is a Lawson-compact algebraic domain.</div></span></li><li><span>(2)</span><span><div>An algebraic domain <em>X</em> is bifinite iff <span><math><mo>[</mo><mi>X</mi><mo>→</mo><mi>L</mi><mo>]</mo></math></span> is a domain for each domain <em>L</em>.</div></span></li><li><span>(3)</span><span><div>The function space from a Lawson-compact algebraic domain to a bifinite domain (not necessarily pointed) is a bifinite domain.</div></span></li></ul></div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"366 ","pages":"Article 109295"},"PeriodicalIF":0.6,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143529236","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}

{"title":"Linear and smooth oriented equivalence of orthogonal representations of finite groups","authors":"Luis Eduardo García-Hernández ,&nbsp;Ben Williams","doi":"10.1016/j.topol.2025.109292","DOIUrl":"10.1016/j.topol.2025.109292","url":null,"abstract":"<div><div>Let Γ be a finite group. We prove that if <span><math><mi>ρ</mi><mo>,</mo><msup><mrow><mi>ρ</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>:</mo><mi>Γ</mi><mo>→</mo><mi>O</mi><mo>(</mo><mn>4</mn><mo>)</mo></math></span> are two representations that are conjugate by an orientation-preserving diffeomorphism of <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>, then they are conjugate by an element of <span><math><mi>SO</mi><mo>(</mo><mn>4</mn><mo>)</mo></math></span>. In the process, we prove that if <span><math><mi>G</mi><mo>⊂</mo><mi>O</mi><mo>(</mo><mn>4</mn><mo>)</mo></math></span> is a finite group, then exactly one of the following is true: the elements of <em>G</em> have a common invariant 1-dimensional subspace in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>4</mn></mrow></msup></math></span>; some element of <em>G</em> has no invariant 1-dimensional subspace; or <em>G</em> is conjugate to a specific group <span><math><mi>K</mi><mo>⊂</mo><mi>O</mi><mo>(</mo><mn>4</mn><mo>)</mo></math></span> of order 16.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"367 ","pages":"Article 109292"},"PeriodicalIF":0.6,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143561853","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}

{"title":"Topological and dimensional properties of univoque bases in double-base expansions","authors":"Yuecai Hu ,&nbsp;Rafael Alcaraz Barrera ,&nbsp;Yuru Zou","doi":"10.1016/j.topol.2025.109294","DOIUrl":"10.1016/j.topol.2025.109294","url":null,"abstract":"<div><div>Given two real numbers <span><math><msub><mrow><mi>q</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>q</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> with <span><math><msub><mrow><mi>q</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>q</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>&gt;</mo><mn>1</mn></math></span> satisfying <span><math><msub><mrow><mi>q</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>+</mo><msub><mrow><mi>q</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>≥</mo><msub><mrow><mi>q</mi></mrow><mrow><mn>0</mn></mrow></msub><msub><mrow><mi>q</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>, we call a sequence <span><math><mo>(</mo><msub><mrow><mi>d</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>)</mo></math></span> with <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>∈</mo><mrow><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>}</mo></mrow></math></span> a <span><math><mo>(</mo><msub><mrow><mi>q</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>q</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></math></span><em>-expansion</em> or a <em>double-base expansion</em> of a real number <em>x</em> if<span><span><span><math><mi>x</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mo>∞</mo></mrow></munderover><mfrac><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow><mrow><msub><mrow><mi>q</mi></mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msub><msub><mrow><mi>q</mi></mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></msub><mo>⋯</mo><msub><mrow><mi>q</mi></mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub></mrow></mfrac><mo>.</mo></math></span></span></span> When <span><math><msub><mrow><mi>q</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><msub><mrow><mi>q</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mi>q</mi></math></span>, the set of <em>univoque bases</em> is given by the set of <em>q</em>'s such that <span><math><mi>x</mi><mo>=</mo><mn>1</mn></math></span> has exactly one <span><math><mo>(</mo><mi>q</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></span>-expansion. The topological, dimensional and symbolic properties of such sets and their corresponding sequences have been intensively investigated. In our research, we study the topological and dimensional properties of the set of univoque bases for double-base expansions. This problem is more complicated, requiring new research strategies. Several new properties are uncovered. In particular, we show that the set of univoque bases in the double base setting is a meagre set with full Hausdorff dimension.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"366 ","pages":"Article 109294"},"PeriodicalIF":0.6,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143551335","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}

{"title":"Singular homology of roots of unity","authors":"Nikola Milićević","doi":"10.1016/j.topol.2025.109291","DOIUrl":"10.1016/j.topol.2025.109291","url":null,"abstract":"<div><div>We extend some basic results from the singular homology theory of topological spaces to the setting of Čech's closure spaces. We prove analogues of the excision and Mayer-Vietoris theorems and the Hurewicz theorem in dimension one. We use these results to calculate examples of singular homology groups of spaces that are not topological but are often encountered in applied topology, such as simple undirected graphs. We focus on the singular homology of roots of unity with closure structures arising from considering nearest neighbors. These examples can then serve as building blocks along with our Mayer-Vietoris and excision theorems for computing the singular homology of more complex closure spaces.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"366 ","pages":"Article 109291"},"PeriodicalIF":0.6,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143509248","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}

{"title":"Many subalgebras of P(ω)/fin","authors":"Klaas Pieter Hart","doi":"10.1016/j.topol.2025.109280","DOIUrl":"10.1016/j.topol.2025.109280","url":null,"abstract":"<div><div>In answer to a question on Mathoverflow we show that the Boolean algebra <span><math><mi>P</mi><mo>(</mo><mi>ω</mi><mo>)</mo><mo>/</mo><mrow><mi>fin</mi></mrow></math></span> contains a family <span><math><mo>{</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>:</mo><mi>X</mi><mo>⊆</mo><mi>c</mi><mo>}</mo></math></span> of subalgebras with the property that <span><math><mi>X</mi><mo>⊆</mo><mi>Y</mi></math></span> implies <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>Y</mi></mrow></msub></math></span> is a subalgebra of <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>X</mi></mrow></msub></math></span> and if <span><math><mi>X</mi><mo>⊈</mo><mi>Y</mi></math></span> then <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>Y</mi></mrow></msub></math></span> is not embeddable into <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>X</mi></mrow></msub></math></span>. The proof proceeds by Stone duality and the construction of a suitable family of separable zero-dimensional compact spaces.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"366 ","pages":"Article 109280"},"PeriodicalIF":0.6,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143509249","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}