Topology and its Applications最新文献

{"title":"Neighborhood system and categorical properties of quasitopological vector spaces","authors":"Zhongqiang Yang ,&nbsp;Yajing Fang ,&nbsp;Qiunan Zheng","doi":"10.1016/j.topol.2025.109281","DOIUrl":"10.1016/j.topol.2025.109281","url":null,"abstract":"<div><div>With the background of diffeological vector spaces endowed with the D-topology, in the paper (Z. Yang and Z. Hu, 2024 <span><span>[14]</span></span>), the authors defined the concept of quasitopological vector space, which is a vector space with a topology satisfying the conditions that the vector addition is separately continuous and the scalar multiplication is continuous. Based on this, in the papers (Z. Yang and Y. Fang, 2024 <span><span>[13]</span></span>) and (Z. Yang and Q. Zheng, 2024 <span><span>[15]</span></span>), the authors continuously discussed this concept. In the present paper, we characterize the quasitopological vector space using the neighborhood system at 0, give the coproducts in the category of quasitopological vector spaces, and the free quasitopological vector space over any topological space.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"365 ","pages":"Article 109281"},"PeriodicalIF":0.6,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143480601","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":"Generalizing β- and λ-maps","authors":"Ana Belén Avilez","doi":"10.1016/j.topol.2025.109282","DOIUrl":"10.1016/j.topol.2025.109282","url":null,"abstract":"<div><div>We generalize the notions of <em>β</em>- and <em>λ</em>-maps in terms of selections of sublocales, obtaining different classes of localic maps. These new classes of maps are used to characterize almost normal, extremally disconnected, <em>F</em>- and <em>Oz</em>-locales, among other types of locales, in a manner akin to the characterization of normal locales via <em>β</em>-maps. As a byproduct we obtain a characterization of localic maps that preserve the completely below relation (that is, the right adjoints of assertive frame homomorphisms).</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"365 ","pages":"Article 109282"},"PeriodicalIF":0.6,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143480604","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":"The mod-2 cohomology groups of low-dimensional unordered flag manifolds and Auerbach bases","authors":"Lorenzo Guerra,&nbsp;Santanil Jana,&nbsp;Arun Maiti","doi":"10.1016/j.topol.2025.109279","DOIUrl":"10.1016/j.topol.2025.109279","url":null,"abstract":"<div><div>Unordered flag manifolds are the manifolds of unordered <em>n</em>-tuple of mutually orthogonal lines in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. In this paper, we develop some basic tools to compute the mod-2 cohomology groups of these spaces and apply them for explicit computation for small <em>n</em>. We show that this computation improves the known estimate of the number of Auerbach bases of normed linear spaces of small dimensions.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"365 ","pages":"Article 109279"},"PeriodicalIF":0.6,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143487492","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":"Almost complex structures on sphere bundles","authors":"G.V. Ambika,&nbsp;B. Subhash","doi":"10.1016/j.topol.2025.109278","DOIUrl":"10.1016/j.topol.2025.109278","url":null,"abstract":"<div><div>In this article, we study the existence of almost complex structures on manifolds that arise as total space of sphere bundles over complex projective spaces and over closed, simply connected 4-manifolds.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"365 ","pages":"Article 109278"},"PeriodicalIF":0.6,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143480600","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":"Symmetric 1-cycles in the deleted product of a graph","authors":"Dzhenzher Ekaterina","doi":"10.1016/j.topol.2025.109277","DOIUrl":"10.1016/j.topol.2025.109277","url":null,"abstract":"<div><div>For a graph <em>K</em>, the deleted product <span><math><mover><mrow><mi>K</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>:</mo><mo>=</mo><mi>K</mi><mo>×</mo><mi>K</mi><mo>∖</mo><mi>diag</mi><mspace></mspace><mi>K</mi></math></span> is the complement to the diagonal diag <em>K</em> in the square <span><math><mi>K</mi><mo>×</mo><mi>K</mi></math></span> of the graph. We describe some 1-cycles generating all symmetric 1-cycles modulo 2 in <span><math><mover><mrow><mi>K</mi></mrow><mrow><mo>˜</mo></mrow></mover></math></span>. The generators are boundaries (of products of disjoint edges in <em>K</em>), off-diagonal cycles (corresponding to the deleted products of simple cycles in <em>K</em>), and triodic cycles (i.e. the deleted products of triods in <em>K</em>). This description is rephrased as a description of generators of the one-dimensional homology group of <span><math><mover><mrow><mi>K</mi></mrow><mrow><mo>˜</mo></mrow></mover></math></span> with <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-coefficients.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"365 ","pages":"Article 109277"},"PeriodicalIF":0.6,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143480599","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":"Relative polar multiplicities and the real link","authors":"David B. Massey","doi":"10.1016/j.topol.2025.109276","DOIUrl":"10.1016/j.topol.2025.109276","url":null,"abstract":"<div><div>For a hypersurface defined by a complex analytic function, we obtain a chain complex of free abelian groups, with ranks given in terms of relative polar multiplicities, which has cohomology isomorphic to the reduced cohomology of the real link. This leads to Morse-type inequalities between the Betti numbers of the real link of the hypersurface and the relative polar multiplicities of the function.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"365 ","pages":"Article 109276"},"PeriodicalIF":0.6,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143474378","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":"On the classifying maps of principal PUn-bundles","authors":"Wen Shen","doi":"10.1016/j.topol.2025.109274","DOIUrl":"10.1016/j.topol.2025.109274","url":null,"abstract":"<div><div>This paper presents the characteristics of homotopy classes of <span><math><mo>[</mo><mi>X</mi><mo>,</mo><msub><mrow><mi>BPU</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>]</mo></math></span> and <span><math><mo>[</mo><mi>X</mi><mo>,</mo><msub><mrow><mi>B</mi><mi>Γ</mi><mi>SU</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>]</mo></math></span> for a certain CW complex <em>X</em>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"363 ","pages":"Article 109274"},"PeriodicalIF":0.6,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143394455","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":"Symmetric monoidal categories of conveniently-constructible Banach bundles","authors":"Alexandru Chirvasitu","doi":"10.1016/j.topol.2025.109273","DOIUrl":"10.1016/j.topol.2025.109273","url":null,"abstract":"<div><div>We show that a continuously-normed Banach bundle <span><math><mi>E</mi></math></span> over a compact Hausdorff space <em>X</em> whose space of sections is algebraically finitely-generated (f.g.) over <span><math><mi>C</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span> is locally trivial (and hence the section space is projective f.g over <span><math><mi>C</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span>); this answers a question of I. Gogić. As a preliminary we also provide sufficient conditions for a quotient bundle to be continuous phrased in terms of the Vietoris continuity of the unit-ball maps attached to the bundles. Related results include (a) the fact that the category of topologically f.g. continuous Banach bundles over <em>X</em> is symmetric monoidal under the (fiber-wise-maximal) tensor product, (b) the full faithfulness of the global-section functor from topologically f.g. continuous bundles to <span><math><mi>C</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span>-modules and (c) the consequent identification of the algebraically f.g. bundles as precisely the rigid objects in the aforementioned symmetric monoidal category.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"363 ","pages":"Article 109273"},"PeriodicalIF":0.6,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143394454","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":"On sequential versions of distributional topological complexity","authors":"Ekansh Jauhari","doi":"10.1016/j.topol.2025.109271","DOIUrl":"10.1016/j.topol.2025.109271","url":null,"abstract":"<div><div>We define a (non-decreasing) sequence <span><math><msub><mrow><mo>{</mo><msub><mrow><mi>dTC</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo><mo>}</mo></mrow><mrow><mi>m</mi><mo>≥</mo><mn>2</mn></mrow></msub></math></span> of sequential versions of distributional topological complexity (<span><math><mi>dTC</mi></math></span>) of a space <em>X</em> introduced by Dranishnikov and Jauhari <span><span>[5]</span></span>. This sequence generalizes <span><math><mi>dTC</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span> in the sense that <span><math><msub><mrow><mi>dTC</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo><mo>=</mo><mi>dTC</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span>, and is a direct analog to the well-known sequence <span><math><msub><mrow><mo>{</mo><msub><mrow><mi>TC</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo><mo>}</mo></mrow><mrow><mi>m</mi><mo>≥</mo><mn>2</mn></mrow></msub></math></span>. We show that like <span><math><msub><mrow><mi>TC</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span> and <span><math><mi>dTC</mi></math></span>, the sequential versions <span><math><msub><mrow><mi>dTC</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span> are also homotopy invariants. Furthermore, <span><math><msub><mrow><mi>dTC</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> relates with the distributional LS-category (<span><math><mi>dcat</mi></math></span>) of products of <em>X</em> in the same way as <span><math><msub><mrow><mi>TC</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> relates with the classical LS-category (<span><math><mi>cat</mi></math></span>) of products of <em>X</em>. On one hand, we show that in general, <span><math><msub><mrow><mi>dTC</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span> is a different concept than <span><math><msub><mrow><mi>TC</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span> for each <span><math><mi>m</mi><mo>≥</mo><mn>2</mn></math></span>. On the other hand, by finding sharp cohomological lower bounds to <span><math><msub><mrow><mi>dTC</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span>, we provide various examples of closed manifolds <em>X</em> for which the sequences <span><math><msub><mrow><mo>{</mo><msub><mrow><mi>TC</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo><mo>}</mo></mrow><mrow><mi>m</mi><mo>≥</mo><mn>2</mn></mrow></msub></math></span> and <span><math><msub><mrow><mo>{</mo><msub><mrow><mi>dTC</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo><mo>}</mo></mrow><mrow><mi>m</mi><mo>≥</mo><mn>2</mn></mrow></msub></math></span> coincide.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"363 ","pages":"Article 109271"},"PeriodicalIF":0.6,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143378592","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":"The separating disk complex for a handlebody","authors":"Sangbum Cho ,&nbsp;Jung Hoon Lee","doi":"10.1016/j.topol.2025.109272","DOIUrl":"10.1016/j.topol.2025.109272","url":null,"abstract":"<div><div>We prove that the separating disk complex for a handlebody is connected. We present two proofs, one is based on the properties of primitive curves while the other one uses the action of the handlebody group on the complex. We also show that the separating reducing sphere complex for a double handlebody is connected.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"363 ","pages":"Article 109272"},"PeriodicalIF":0.6,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143349678","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}