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The Nielsen realization problem for non-orientable surfaces 不可定向曲面的尼尔森实现问题
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-05-16 DOI: 10.1016/j.topol.2024.108957
Nestor Colin , Miguel A. Xicoténcatl
{"title":"The Nielsen realization problem for non-orientable surfaces","authors":"Nestor Colin ,&nbsp;Miguel A. Xicoténcatl","doi":"10.1016/j.topol.2024.108957","DOIUrl":"10.1016/j.topol.2024.108957","url":null,"abstract":"<div><p>We show the Teichmüller space of a non-orientable surface with marked points (considered as a Klein surface) can be identified with a subspace of the Teichmüller space of its orientable double cover. It is also well known that the mapping class group <span><math><mi>Mod</mi><mo>(</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>g</mi></mrow></msub><mo>;</mo><mi>k</mi><mo>)</mo></math></span> of a non-orientable surface can be identified with a subgroup of <span><math><mi>Mod</mi><mo>(</mo><msub><mrow><mi>S</mi></mrow><mrow><mi>g</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>;</mo><mn>2</mn><mi>k</mi><mo>)</mo></math></span>, the mapping class group of its orientable double cover. These facts, together with the classical Nielsen realization theorem, are used to prove that every finite subgroup of <span><math><mi>Mod</mi><mo>(</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>g</mi></mrow></msub><mo>;</mo><mi>k</mi><mo>)</mo></math></span> can be lifted isomorphically to a subgroup of the group of diffeomorphisms <span><math><mi>Diff</mi><mo>(</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>g</mi></mrow></msub><mo>;</mo><mi>k</mi><mo>)</mo></math></span>. In contrast, we show the projection <span><math><mi>Diff</mi><mo>(</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>g</mi></mrow></msub><mo>)</mo><mo>→</mo><mi>Mod</mi><mo>(</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>g</mi></mrow></msub><mo>)</mo></math></span> does not admit a section for large <em>g</em>.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141146614","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
Blowdown, k-wedge and evenness of quasitoric orbifolds 准轨道折线的坍缩、K边和偶数性
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-05-15 DOI: 10.1016/j.topol.2024.108953
Koushik Brahma, Soumen Sarkar, Subhankar Sau
{"title":"Blowdown, k-wedge and evenness of quasitoric orbifolds","authors":"Koushik Brahma,&nbsp;Soumen Sarkar,&nbsp;Subhankar Sau","doi":"10.1016/j.topol.2024.108953","DOIUrl":"10.1016/j.topol.2024.108953","url":null,"abstract":"<div><p>In this paper, we introduce polytopal <em>k</em>-wedge construction and blowdown of a simple polytope and inspect the effect on the retraction sequence of a simple polytope due to the <em>k</em>-wedge construction and blowdown. In relation to these constructions, we introduce the <em>k</em>-wedge and blowdown of a quasitoric orbifold. We compare the torsions in the integral cohomologies of <em>k</em>-wedges and blowdowns of a quasitoric orbifold with the original one. These two constructions provide infinitely many integrally equivariantly formal quasitoric orbifolds from a given one.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141054424","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
Cardinal functions on lexicographic products 词典积上的红心功能
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-05-14 DOI: 10.1016/j.topol.2024.108954
Yasushi Hirata , Nobuyuki Kemoto
{"title":"Cardinal functions on lexicographic products","authors":"Yasushi Hirata ,&nbsp;Nobuyuki Kemoto","doi":"10.1016/j.topol.2024.108954","DOIUrl":"10.1016/j.topol.2024.108954","url":null,"abstract":"<div><p>We will calculate the density, the spread and related cardinal functions on lexicographic products of GO-spaces, and give their applications.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0166864124001391/pdfft?md5=be3040e771ae19dd88d90464cb8f6b06&pid=1-s2.0-S0166864124001391-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141040656","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
Continuity of operations in right semitopological groups 右半拓扑群中运算的连续性
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-05-14 DOI: 10.1016/j.topol.2024.108952
Evgenii Reznichenko
{"title":"Continuity of operations in right semitopological groups","authors":"Evgenii Reznichenko","doi":"10.1016/j.topol.2024.108952","DOIUrl":"10.1016/j.topol.2024.108952","url":null,"abstract":"<div><p>Groups with a topology that is in consistent one way or another with the algebraic structure are considered. Well-known classes of groups with a topology are topological, paratopological, semitopological, and quasitopological groups. We also study other ways of matching topology and algebraic structure. The minimum requirement in this paper is that the group is a right semitopological group (such groups are often called right topological groups). We study when a group with a topology is a topological group; research in this direction began with the work of Deane Montgomery and Robert Ellis. (Invariant) semi-neighborhoods of the diagonal are used as a means of study.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141038588","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
A survey of generalized metrizable properties in topological groups and weakly topological groups 拓扑群和弱拓扑群中的广义元可性质概览
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-05-09 DOI: 10.1016/j.topol.2024.108944
Shou Lin , Xuewei Ling , Xin Liu
{"title":"A survey of generalized metrizable properties in topological groups and weakly topological groups","authors":"Shou Lin ,&nbsp;Xuewei Ling ,&nbsp;Xin Liu","doi":"10.1016/j.topol.2024.108944","DOIUrl":"10.1016/j.topol.2024.108944","url":null,"abstract":"<div><p>The theory of generalized metrizable spaces is an important topic of general topology. This paper is a survey of research methods and achievements on generalized metrizable properties in topological groups and weakly topological groups. We mainly study this kind of properties in topological groups, semitopological groups, paratopological groups, quasitopological groups and free topological groups, and focus on the influence of separation properties, conditions for weakly topological groups to become topological groups, cardinal invariants, weak first-countability, three-space properties and remainders in compactifications on topological groups and related structures. Finally, some unsolved problems in this field are listed for researchers.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140930996","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
On semi-stratifiable frames 关于半可变框架
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-05-08 DOI: 10.1016/j.topol.2024.108943
Er-Guang Yang
{"title":"On semi-stratifiable frames","authors":"Er-Guang Yang","doi":"10.1016/j.topol.2024.108943","DOIUrl":"10.1016/j.topol.2024.108943","url":null,"abstract":"<div><p>In this paper, we introduce the notion of a semi-stratifiable frame as an extension of classical semi-stratifiability and also as the monotonization of perfect frames. We show that stratifiable frames are precisely the monotonically normal semi-stratifiable frames. Moreover, we present an insertion theorem for semi-stratifiable frames in terms of real functions and thereby obtain an insertion theorem for stratifiable frames.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140930993","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
Convergent sequences in iterated ultrapowers as p-compact groups 作为 p 紧密群的迭代超幂中的收敛序列
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-05-08 DOI: 10.1016/j.topol.2024.108932
Ulises Ariet Ramos-García , David Valencia-Gómez
{"title":"Convergent sequences in iterated ultrapowers as p-compact groups","authors":"Ulises Ariet Ramos-García ,&nbsp;David Valencia-Gómez","doi":"10.1016/j.topol.2024.108932","DOIUrl":"10.1016/j.topol.2024.108932","url":null,"abstract":"<div><p>We prove, in <span><math><mi>ZFC</mi></math></span>, that if <span><math><mi>G</mi></math></span> is an infinite countable Abelian group, then there is an ultrafilter <span><math><mi>p</mi><mo>∈</mo><msup><mrow><mi>ω</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> such that <span><math><mo>(</mo><msub><mrow><mi>Ult</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo><mo>,</mo><msub><mrow><mi>τ</mi></mrow><mrow><mover><mrow><mtext>Bohr</mtext></mrow><mo>‾</mo></mover></mrow></msub><mo>)</mo></math></span> has non-trivial convergent sequences, consequently <span><math><mo>(</mo><msubsup><mrow><mi>Ult</mi></mrow><mrow><mi>p</mi></mrow><mrow><msub><mrow><mi>ω</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msubsup><mo>(</mo><mi>G</mi><mo>)</mo><mo>,</mo><msub><mrow><mi>τ</mi></mrow><mrow><mover><mrow><mtext>Bohr</mtext></mrow><mo>‾</mo></mover></mrow></msub><mo>)</mo></math></span> has non-trivial convergent sequences, extending Theorem 3.9 from <span>[13]</span>. In addition, we prove that the Remark 3.8 from <span>[13]</span> is false; so, the proof of the Corollary 3.11 is false too.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140935958","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
Characterizing some topological spaces with set-valued maps to a space with an original point 一些具有原点空间集值映射的拓扑空间的特征
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-05-08 DOI: 10.1016/j.topol.2024.108940
Er-Guang Yang
{"title":"Characterizing some topological spaces with set-valued maps to a space with an original point","authors":"Er-Guang Yang","doi":"10.1016/j.topol.2024.108940","DOIUrl":"https://doi.org/10.1016/j.topol.2024.108940","url":null,"abstract":"<div><p>In this paper, the notion of an original point for a topological space is introduced. Then characterizations of some spaces such as stratifiable spaces and MCP-spaces in terms of set-valued maps with values in <span><math><mi>F</mi><mo>(</mo><mi>Y</mi><mo>)</mo></math></span>, where <em>Y</em> has an original point, are presented.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0166864124001251/pdfft?md5=9c66fbb4c11eb98dcb7bfbff9b1e7dec&pid=1-s2.0-S0166864124001251-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140918294","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
Properties of arithmetics progressions in increasing sequence of T0-topologies on the set of positive integers 正整数集合上 T0 拓扑递增序列中算术级数的性质
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-05-07 DOI: 10.1016/j.topol.2024.108939
Dawid Krasiński, Paulina Szyszkowska
{"title":"Properties of arithmetics progressions in increasing sequence of T0-topologies on the set of positive integers","authors":"Dawid Krasiński,&nbsp;Paulina Szyszkowska","doi":"10.1016/j.topol.2024.108939","DOIUrl":"https://doi.org/10.1016/j.topol.2024.108939","url":null,"abstract":"<div><p>In this paper we continue researches deal with increasing sequence <span><math><mo>{</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>}</mo></math></span> of <span><math><msub><mrow><mi>T</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>-topologies on the set of positive integers focusing on the properties of arithmetic progressions in topologies <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span>. We characterize the closures of arithmetic progressions in all topologies <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span> on <span><math><mi>N</mi></math></span>. Additionally, we present the characterization of the closures of arithmetic progressions in the common division topology <span><math><mi>T</mi></math></span> on <span><math><mi>N</mi></math></span>. Moreover, for each <span><math><mi>m</mi><mo>∈</mo><mi>N</mi></math></span> we characterize regular open arithmetic progressions in <span><math><mo>(</mo><mi>N</mi><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>)</mo></math></span> and we examine which of these spaces are semiregular.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S016686412400124X/pdfft?md5=e0f5962274f193e430014a7bae207796&pid=1-s2.0-S016686412400124X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140951292","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 number of nested twice-punctured tori in a hyperbolic knot exterior 论双曲结外部嵌套两次穿刺环的数量
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-05-07 DOI: 10.1016/j.topol.2024.108938
Román Aranda , Enrique Ramírez-Losada , Jesús Rodríguez-Viorato
{"title":"On the number of nested twice-punctured tori in a hyperbolic knot exterior","authors":"Román Aranda ,&nbsp;Enrique Ramírez-Losada ,&nbsp;Jesús Rodríguez-Viorato","doi":"10.1016/j.topol.2024.108938","DOIUrl":"https://doi.org/10.1016/j.topol.2024.108938","url":null,"abstract":"<div><p>This paper continues a program due to Motegi regarding universal bounds for the number of nonisotopic essential <em>n</em>-punctured tori in the complement of a hyperbolic knot in <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. For <span><math><mi>n</mi><mo>=</mo><mn>1</mn></math></span>, Valdez-Sánchez showed that there are at most five nonisotopic Seifert tori in the exterior of a hyperbolic knot. In this paper, we address the case <span><math><mi>n</mi><mo>=</mo><mn>2</mn></math></span>. We show that there are at most six nonisotopic, nested, essential 2-holed tori in the complement of every hyperbolic knot.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140951293","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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