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On cofinite topologies on posets, chains in subfit frames, and subfit irreducible frames 关于偏序集、子拟合框架中的链和子拟不可约框架上的有限拓扑
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-04-01 DOI: 10.1016/j.topol.2025.109380
M. Andrew Moshier , Aleš Pultr
{"title":"On cofinite topologies on posets, chains in subfit frames, and subfit irreducible frames","authors":"M. Andrew Moshier ,&nbsp;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}
引用次数: 0
Relative hyperbolicity of graphical small cancellation groups 图示小消去群的相对双曲性
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-04-01 DOI: 10.1016/j.topol.2025.109381
Suzhen Han
{"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}
引用次数: 0
Circularly chainable continua that annularly inscribe squares 环状刻划正方形的可循环链连续体
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-27 DOI: 10.1016/j.topol.2025.109379
Ulises Morales-Fuentes , Cristina Villanueva-Segovia
{"title":"Circularly chainable continua that annularly inscribe squares","authors":"Ulises Morales-Fuentes ,&nbsp;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}
引用次数: 0
On the fundamental groups of solenoid complements in S3 论S3中螺线管补体的基本群
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-27 DOI: 10.1016/j.topol.2025.109377
Xueming Hui
{"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}
引用次数: 0
Special issue dedicated to Iberoamerican and Pan Pacific International Conference on Topology and its Applications, Benemérita Universidad Autónoma de Puebla, Ciudad de Puebla, México, September 2023 特刊致力于伊比利亚美洲和泛太平洋国际会议上拓扑及其应用,Benemerita普埃布拉大学之城普埃布拉,墨西哥,2023年9月
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-26 DOI: 10.1016/j.topol.2025.109347
Mario Eudave-Muñoz (Guest Editor), Juan José Font (Guest Editor), Salvador García-Ferreira (Guest Editor), Yasunao Hattori (Guest Editor), Rodrigo Hernández Gutiérrez (Guest Editor), Ángel Tamariz-Mascarúa (Guest Editor)
{"title":"Special issue dedicated to Iberoamerican and Pan Pacific International Conference on Topology and its Applications, Benemérita Universidad Autónoma de Puebla, Ciudad de Puebla, México, September 2023","authors":"Mario Eudave-Muñoz (Guest Editor),&nbsp;Juan José Font (Guest Editor),&nbsp;Salvador García-Ferreira (Guest Editor),&nbsp;Yasunao Hattori (Guest Editor),&nbsp;Rodrigo Hernández Gutiérrez (Guest Editor),&nbsp;Ángel Tamariz-Mascarúa (Guest Editor)","doi":"10.1016/j.topol.2025.109347","DOIUrl":"10.1016/j.topol.2025.109347","url":null,"abstract":"","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"371 ","pages":"Article 109347"},"PeriodicalIF":0.6,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144632019","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
Hausdorff distance of univoque sets 唯一集的豪斯多夫距离
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-26 DOI: 10.1016/j.topol.2025.109378
Yi Cai , Vilmos Komornik
{"title":"Hausdorff distance of univoque sets","authors":"Yi Cai ,&nbsp;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}
引用次数: 0
Equivariant K-theory of even-dimensional complex quadrics 偶维复二次曲面的等变k理论
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-25 DOI: 10.1016/j.topol.2025.109376
Bidhan Paul
{"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}
引用次数: 0
Flipping Heegaard splittings of Seifert fibered spaces 翻转，防止纤维空间的分裂
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-25 DOI: 10.1016/j.topol.2025.109375
Jennifer Schultens
{"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}
引用次数: 0
On keen bridge splittings of links 在敏锐的桥梁上分裂的链接
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-24 DOI: 10.1016/j.topol.2025.109355
Ayako Ido , Yeonhee Jang , Tsuyoshi Kobayashi
{"title":"On keen bridge splittings of links","authors":"Ayako Ido ,&nbsp;Yeonhee Jang ,&nbsp;Tsuyoshi Kobayashi","doi":"10.1016/j.topol.2025.109355","DOIUrl":"10.1016/j.topol.2025.109355","url":null,"abstract":"<div><div>In this paper, we extend the concept of <em>(strong) keenness</em> for Heegaard splittings to bridge splittings, and show that, for any integers <em>g</em>, <em>b</em> and <em>n</em> with <span><math><mi>g</mi><mo>≥</mo><mn>0</mn></math></span>, <span><math><mi>b</mi><mo>≥</mo><mn>1</mn></math></span>, <span><math><mi>n</mi><mo>≥</mo><mn>1</mn></math></span> except for <span><math><mo>(</mo><mi>g</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span> and <span><math><mo>(</mo><mi>g</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>n</mi><mo>)</mo><mo>=</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>, there exists a strongly keen <span><math><mo>(</mo><mi>g</mi><mo>,</mo><mi>b</mi><mo>)</mo></math></span>-splitting of a link with distance <em>n</em>. We also show that any <span><math><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></span>-splitting of a link with distance 1 cannot be keen.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"371 ","pages":"Article 109355"},"PeriodicalIF":0.6,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144631909","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
Dibiquandle coloring invariants for dichromatic links and associated di(bi)quandles 二色环及相关二（二）环的双双环着色不变量
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-24 DOI: 10.1016/j.topol.2025.109358
Jieon Kim , Sang Youl Lee , Mohd Ibrahim Sheikh
{"title":"Dibiquandle coloring invariants for dichromatic links and associated di(bi)quandles","authors":"Jieon Kim ,&nbsp;Sang Youl Lee ,&nbsp;Mohd Ibrahim Sheikh","doi":"10.1016/j.topol.2025.109358","DOIUrl":"10.1016/j.topol.2025.109358","url":null,"abstract":"<div><div>In this paper, we introduce the notion of a dibiquandle which comes from coupling two biquandle structures which interact via a kind of distributive laws and set up dibiquandle counting invariant for dichromatic links. We present explicit constructions of free dibiquandles, presentations of dibiquandles and Tietze transformations. Then we define the fundamental dibiquandles for dichromatic links and discuss enhancements of the dibiquandle counting invariant. Further, we introduce the associated diquandle of a dibiquandle and use it to explore the relationship between dibiquandles and diquandles. As the main application, we formulate the fundamental dibiquandles and dibiquandle counting invariants for knots and links in the solid torus <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>×</mo><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>. In addition, we provide an enumeration of all finite dibiquandles of orders ≤3 up to isomorphism.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"371 ","pages":"Article 109358"},"PeriodicalIF":0.6,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144631912","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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