{"title":"Q-points in the Tukey order","authors":"Dilip Raghavan","doi":"10.1016/j.topol.2025.109423","DOIUrl":"10.1016/j.topol.2025.109423","url":null,"abstract":"<div><div>Q-points are cofinal in the RK-ordering under several mild hypotheses.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"370 ","pages":"Article 109423"},"PeriodicalIF":0.6,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144107584","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}
Wayne A. Johnson , Dae-Woong Lee , P. Christopher Staecker
{"title":"On digital H-spaces","authors":"Wayne A. Johnson , Dae-Woong Lee , P. Christopher Staecker","doi":"10.1016/j.topol.2025.109426","DOIUrl":"10.1016/j.topol.2025.109426","url":null,"abstract":"<div><div>We investigate properties of digital H-spaces in the graph theoretic model of digital topology. As in prior work, the results obtained often depend fundamentally on the choice between <span><math><msub><mrow><mi>NP</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>NP</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> product adjacencies. We explore algebraic properties of digital H-spaces preserved under digital homotopy equivalence, and we give a general construction that produces examples of digital H-spaces that are not homotopy-equivalent to digital topological groups in both categories. Further, we show that this construction essentially classifies all <span><math><msub><mrow><mi>NP</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-digital H-spaces. In a short appendix, we resolve a question that was left unresolved in <span><span>[16]</span></span>, and complete the full classification of digital topological groups.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"370 ","pages":"Article 109426"},"PeriodicalIF":0.6,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144107583","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":"Minimality of the inner automorphism group","authors":"D. Peng , Menachem Shlossberg","doi":"10.1016/j.topol.2025.109425","DOIUrl":"10.1016/j.topol.2025.109425","url":null,"abstract":"<div><div>By <span><span>[7]</span></span>, a minimal group <em>G</em> is called <em>z-minimal</em> if <span><math><mi>G</mi><mo>/</mo><mi>Z</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> is minimal. In this paper, we present the <em>z-Minimality Criterion</em> for dense subgroups. For a locally compact group <em>G</em>, let <span><math><mi>Inn</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> be the group of all inner automorphisms of <em>G</em>, endowed with the Birkhoff topology. Using a theorem by Goto <span><span>[15]</span></span>, we obtain our main result which asserts that if <em>G</em> is a connected Lie group and <span><math><mi>H</mi><mo>∈</mo><mo>{</mo><mi>G</mi><mo>/</mo><mi>Z</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>,</mo><mi>Inn</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>}</mo></math></span>, then <em>H</em> is minimal if and only if <em>H</em> is centre-free and topologically isomorphic to <span><math><mi>Inn</mi><mo>(</mo><mi>G</mi><mo>/</mo><mi>Z</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>)</mo></math></span>. In particular, if <em>G</em> is a connected Lie group with discrete centre, then <span><math><mi>Inn</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> is minimal. We prove that a connected locally compact nilpotent group is <em>z</em>-minimal if and only if it is compact abelian. In contrast, we show that there exists a connected metabelian <em>z</em>-minimal Lie group that is neither compact nor abelian. As in the papers <span><span>[27]</span></span>, <span><span>[33]</span></span>, some applications to Number Theory are provided.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"370 ","pages":"Article 109425"},"PeriodicalIF":0.6,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144068265","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":"Algebraic topology of certain Sasaki joins","authors":"Candelario Castañeda, Ross Staffeldt","doi":"10.1016/j.topol.2025.109422","DOIUrl":"10.1016/j.topol.2025.109422","url":null,"abstract":"<div><div>The join construction produces a third Sasaki manifold from two others, and we investigate the algebraic topology of the joins of circle bundles over surfaces of positive genus with weighted three-spheres. Topologically, such a join has the structure of a lens space bundle over a surface. We calculate invariants determined by the fundamental group, the homology, and the cohomology. We find that, in general, there is torsion in the integral homology of the join. The torsion gives rise to two linking forms, and we identify these linking forms.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"370 ","pages":"Article 109422"},"PeriodicalIF":0.6,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144089460","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":"Knot exteriors with all compact surfaces of positive genus essentially embedded","authors":"João M. Nogueira","doi":"10.1016/j.topol.2025.109421","DOIUrl":"10.1016/j.topol.2025.109421","url":null,"abstract":"<div><div>It is well known that there exist knots with Seifert surfaces of arbitrarily high genus. In this paper, we show the existence of infinitely many knot exteriors where each of which has longitudinal essential surfaces of any positive genus and any number of boundary components.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"370 ","pages":"Article 109421"},"PeriodicalIF":0.6,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144068264","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":"Gyration stability for projective planes","authors":"Sebastian Chenery , Stephen Theriault","doi":"10.1016/j.topol.2025.109420","DOIUrl":"10.1016/j.topol.2025.109420","url":null,"abstract":"<div><div>Gyrations are operations on manifolds that arise in geometric topology, where a manifold <em>M</em> may exhibit distinct gyrations depending on the chosen twisting. For a given <em>M</em>, we ask a natural question: do all gyrations of <em>M</em> share the same homotopy type regardless of the twisting? A manifold with this property is said to have gyration stability. Inspired by recent work by Duan, which demonstrated that the quaternionic projective plane is not gyration stable with respect to diffeomorphism, we explore this question for projective planes in general. We obtain a complete description of gyration stability for the complex, quaternionic, and octonionic projective planes up to homotopy.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"369 ","pages":"Article 109420"},"PeriodicalIF":0.6,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143937563","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":"Set (strongly) star Scheepers spaces","authors":"Fortunato Maesano","doi":"10.1016/j.topol.2025.109409","DOIUrl":"10.1016/j.topol.2025.109409","url":null,"abstract":"<div><div>In this article, two new covering properties are analyzed, formulated starting from the combinatorial approach to the covering properties; after having determined the relationships with properties known in the literature and being distinguished from them, their inheritance with respect to the subspaces, the behavior with respect to the product and the relationships with particular spaces in the literature are investigated.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"370 ","pages":"Article 109409"},"PeriodicalIF":0.6,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143936489","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":"Remetrizing dynamical systems to control distances of points in time","authors":"Krzysztof Gołębiowski","doi":"10.1016/j.topol.2025.109419","DOIUrl":"10.1016/j.topol.2025.109419","url":null,"abstract":"<div><div>Main aim of this article is to prove that for any continuous function <span><math><mi>f</mi><mo>:</mo><mi>X</mi><mo>→</mo><mi>X</mi></math></span>, where <em>X</em> is metrizable (or, more generally, for any family <span><math><mi>F</mi></math></span> of such functions, with one extra condition), there exists a compatible metric <em>d</em> on <em>X</em> such that the nth iteration of <em>f</em> (more generally, composition of any <em>n</em> functions from <span><math><mi>F</mi></math></span>) is Lipschitz with constant <span><math><msub><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> where <span><math><msubsup><mrow><mo>(</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></mrow><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mo>∞</mo></mrow></msubsup></math></span> is an arbitrarily fixed sequence of real numbers such that <span><math><mn>1</mn><mo><</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> and <span><math><munder><mi>lim</mi><mrow><mi>n</mi><mo>→</mo><mo>+</mo><mo>∞</mo></mrow></munder><mo></mo><msub><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>=</mo><mo>+</mo><mo>∞</mo></math></span>. In particular, any dynamical system can be remetrized in order to significantly control the distance between points by their initial distance.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"370 ","pages":"Article 109419"},"PeriodicalIF":0.6,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143936491","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":"Planar equivalence of knotoids and quandle invariants","authors":"Mohamed Elhamdadi , Wout Moltmaker , Masahico Saito","doi":"10.1016/j.topol.2025.109407","DOIUrl":"10.1016/j.topol.2025.109407","url":null,"abstract":"<div><div>While knotoids on the sphere are well-understood by a variety of invariants, knotoids on the plane have proven more subtle to classify due to their multitude over knotoids on the sphere and a lack of invariants that detect a diagram's planar nature. In this paper, we investigate equivalence of planar knotoids using quandle colorings and cocycle invariants. These quandle invariants are able to detect planarity by considering quandle colorings that are restricted at distinguished points in the diagram, namely the endpoints and the point-at-infinity. After defining these invariants we consider their applications to symmetry properties of planar knotoids such as invertibility and chirality. Furthermore we introduce an invariant called the triangular quandle cocycle invariant and show that it is a stronger invariant than the end specified quandle colorings.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"369 ","pages":"Article 109407"},"PeriodicalIF":0.6,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143937561","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":"Spaces of metrics are Baire","authors":"Yoshito Ishiki","doi":"10.1016/j.topol.2025.109408","DOIUrl":"10.1016/j.topol.2025.109408","url":null,"abstract":"<div><div>For a metrizable space, we consider the space of all metrics generating the same topology of the metrizable space, and this space of metrics is equipped with the supremum metric. In this paper, for every metrizable space, we establish that the space of metrics on the metrizable space is Baire. We also show that the set of all complete metrics is comeager in the space of metrics. Moreover, we investigate non–Archimedean analogues of these results. As an application, we prove that typical metrics take typical reals.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"369 ","pages":"Article 109408"},"PeriodicalIF":0.6,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143922804","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}
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