{"title":"Isometries of spaces of compact convex subsets of Busemann spaces","authors":"Kacper Kazimierz Kurowski","doi":"10.1016/j.topol.2025.109385","DOIUrl":"10.1016/j.topol.2025.109385","url":null,"abstract":"<div><div>We prove that every surjective isometry between the spaces of nonempty compact geodesically convex subsets of certain geodesically complete Busemann spaces, endowed with the Hausdorff metric, is induced by an isometry between the underlying spaces.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"368 ","pages":"Article 109385"},"PeriodicalIF":0.6,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143828198","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":"Exotic 4-manifolds with small trisection genus","authors":"Natsuya Takahashi","doi":"10.1016/j.topol.2025.109382","DOIUrl":"10.1016/j.topol.2025.109382","url":null,"abstract":"<div><div>We show that there exists an exotic pair of 4-manifolds with boundary whose trisection genera are 4. We also construct genus-3 relative trisections for an infinite family of contractible 4-manifolds introduced by Akbulut and Kirby.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"368 ","pages":"Article 109382"},"PeriodicalIF":0.6,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143799358","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 cofinite topologies on posets, chains in subfit frames, and subfit irreducible frames","authors":"M. Andrew Moshier , Aleš Pultr","doi":"10.1016/j.topol.2025.109380","DOIUrl":"10.1016/j.topol.2025.109380","url":null,"abstract":"<div><div>We prove that (1) each well-ordered chain is a dense sublocale of a subfit frame, and (2) that an irreducible frame (a frame that cannot be decomposed into two smaller closed sublocales) can be subfit (although it cannot be fit or even prefit). The basic tool is to use order-cofinite topologies on posets (also known as weak topologies); we discuss these in some more detail, for instance showing their relation with the Bruns-Lakser hull.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"368 ","pages":"Article 109380"},"PeriodicalIF":0.6,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143785842","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 hyperbolicity of graphical small cancellation groups","authors":"Suzhen Han","doi":"10.1016/j.topol.2025.109381","DOIUrl":"10.1016/j.topol.2025.109381","url":null,"abstract":"<div><div>A piece of a labelled graph Γ refers to a labelled path that embeds into Γ in two different ways up to label-preserving automorphisms. We prove that graphical <span><math><mi>G</mi><msup><mrow><mi>r</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>6</mn></mrow></mfrac><mo>)</mo></math></span> small cancellation groups whose associated pieces have uniformly bounded length are relatively hyperbolic. In fact, we show that the Cayley graph of such a group presentation is asymptotically tree-graded with respect to the collection of all embedded components of the defining graph Γ, if and only if the lengths of pieces of Γ are uniformly bounded. This implies the relative hyperbolicity by a characterization given by Druţu, Osin and Sapir.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"368 ","pages":"Article 109381"},"PeriodicalIF":0.6,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143799357","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":"Circularly chainable continua that annularly inscribe squares","authors":"Ulises Morales-Fuentes , Cristina Villanueva-Segovia","doi":"10.1016/j.topol.2025.109379","DOIUrl":"10.1016/j.topol.2025.109379","url":null,"abstract":"<div><div>Let <em>A</em> denote the annulus <span><math><mo>{</mo><mi>x</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>:</mo><mn>1</mn><mo>≤</mo><mo>|</mo><mo>|</mo><mi>x</mi><mo>|</mo><mo>|</mo><mo>≤</mo><mn>1</mn><mo>+</mo><msqrt><mrow><mn>2</mn></mrow></msqrt><mo>}</mo></math></span>. In this paper we prove that if <em>X</em> is a circularly chainable continuum essentially embedded in <em>A</em>, then <em>X</em> contains the four vertices of an Euclidean square of side length at least <span><math><msqrt><mrow><mn>2</mn></mrow></msqrt></math></span>. Furthermore, let us say that a plane continuum <em>X</em> satisfies the property of annular inscription in <em>A</em> if whenever <em>X</em> is essentially embedded in <em>A</em>, the image of such embedding admits an inscribed square of side length at least <span><math><msqrt><mrow><mn>2</mn></mrow></msqrt></math></span>. We show that every circularly chainable, not chainable plane continuum satisfies the property of annular inscription in <em>A</em> and, moreover, that the property of annular inscription in <em>A</em> is generic among continua that separate the plane.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"368 ","pages":"Article 109379"},"PeriodicalIF":0.6,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143792540","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 fundamental groups of solenoid complements in S3","authors":"Xueming Hui","doi":"10.1016/j.topol.2025.109377","DOIUrl":"10.1016/j.topol.2025.109377","url":null,"abstract":"<div><div>We show that the fundamental groups of the complements of knotted solenoids in <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> are solely determined by a canonical sequence of knot groups. Moreover, they are determined by the solenoid embeddings in <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> up to the mirror image.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"368 ","pages":"Article 109377"},"PeriodicalIF":0.6,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143777563","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":"Hausdorff distance of univoque sets","authors":"Yi Cai , Vilmos Komornik","doi":"10.1016/j.topol.2025.109378","DOIUrl":"10.1016/j.topol.2025.109378","url":null,"abstract":"<div><div>Since their introduction by Rényi <span><span>[21]</span></span>, expansions in non-integer bases have been investigated abundantly. It was discovered by Erdős et al. <span><span>[10]</span></span>, <span><span>[11]</span></span> that, contrary to the case of integer bases, the sets of numbers with a unique expansion have a surprisingly complex structure. The present paper is devoted to the continuity properties of these sets with respect to the base.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"368 ","pages":"Article 109378"},"PeriodicalIF":0.6,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143785841","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":"Equivariant K-theory of even-dimensional complex quadrics","authors":"Bidhan Paul","doi":"10.1016/j.topol.2025.109376","DOIUrl":"10.1016/j.topol.2025.109376","url":null,"abstract":"<div><div>The aim of this paper is to describe the torus equivariant <em>K</em>-ring of even-dimensional complex quadrics by studying the graph equivariant <em>K</em>-theory of their corresponding GKM graphs. This involves providing a presentation for its graph equivariant <em>K</em>- ring in terms of generators and relations. This parallels the description of the equivariant cohomology ring of even-dimensional complex quadrics due to Kuroki.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"368 ","pages":"Article 109376"},"PeriodicalIF":0.6,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143737937","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":"Flipping Heegaard splittings of Seifert fibered spaces","authors":"Jennifer Schultens","doi":"10.1016/j.topol.2025.109375","DOIUrl":"10.1016/j.topol.2025.109375","url":null,"abstract":"<div><div>A Heegaard splitting of a 3-manifold is flippable if there is an isotopy that interchanges the two sides of the Heegaard splitting. We explore which Heegaard splittings of Seifert fibered spaces are flippable and which are not.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"368 ","pages":"Article 109375"},"PeriodicalIF":0.6,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759804","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}
Toky Andriamanalina , Myfanwy E. Evans , Sonia Mahmoudi
{"title":"Diagrammatic representations of 3-periodic entanglements","authors":"Toky Andriamanalina , Myfanwy E. Evans , Sonia Mahmoudi","doi":"10.1016/j.topol.2025.109346","DOIUrl":"10.1016/j.topol.2025.109346","url":null,"abstract":"<div><div>Diagrams enable the use of various algebraic and geometric tools for analysing and classifying knots. In this paper we introduce a new diagrammatic representation of triply periodic entangled structures (<em>TP tangles</em>), which are embeddings of simple curves in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> that are invariant under translations along three non-coplanar axes. As such, these entanglements can be seen as preimages of links embedded in the 3-torus <span><math><msup><mrow><mi>T</mi></mrow><mrow><mn>3</mn></mrow></msup><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><mo>×</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> in its universal cover <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>, where two non-isotopic links in <span><math><msup><mrow><mi>T</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> may possess the same TP tangle preimage. We consider the equivalence of TP tangles in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> through the use of diagrams representing links in <span><math><msup><mrow><mi>T</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. These diagrams require additional moves beyond the classical Reidemeister moves, which we define and show that they preserve ambient isotopies of links in <span><math><msup><mrow><mi>T</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. The final definition of a <em>tridiagram</em> of a link in <span><math><msup><mrow><mi>T</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> allows us to then consider additional notions of equivalence relating non-isotopic links in <span><math><msup><mrow><mi>T</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> that possess the same TP tangle preimage.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"368 ","pages":"Article 109346"},"PeriodicalIF":0.6,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759805","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}
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