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A crossed homomorphism for groups acting on the circle 作用于圆的群的交叉同构
IF 0.8 3区 数学
Journal of Topology and Analysis Pub Date : 2024-02-05 DOI: 10.1142/s1793525324500092
Shuhei Maruyama
{"title":"A crossed homomorphism for groups acting on the circle","authors":"Shuhei Maruyama","doi":"10.1142/s1793525324500092","DOIUrl":"https://doi.org/10.1142/s1793525324500092","url":null,"abstract":"<p>In this paper, we construct a crossed homomorphism by using a group action on the circle and the Poincaré translation number. We relate it to the Euler class of the action in terms of the Hochschild–Serre spectral sequence. As an application, we answer a question of Calegari and Chen, which is on an explicit form of a certain crossed homomorphism on the mapping class group of the sphere minus a Cantor set.</p>","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":"152 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140166952","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Analytic automorphism group and similar representation of analytic functions 解析自变群和解析函数的相似表示
IF 0.8 3区 数学
Journal of Topology and Analysis Pub Date : 2024-01-05 DOI: 10.1142/s1793525324500043
Bingzhe Hou, Chunlan Jiang
{"title":"Analytic automorphism group and similar representation of analytic functions","authors":"Bingzhe Hou, Chunlan Jiang","doi":"10.1142/s1793525324500043","DOIUrl":"https://doi.org/10.1142/s1793525324500043","url":null,"abstract":"","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":"87 8","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139450119","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Morse homology for perturbed Dirac-harmonic maps into flat tori 进入平面环的扰动狄拉克谐波映射的莫尔斯同源性
IF 0.8 3区 数学
Journal of Topology and Analysis Pub Date : 2024-01-05 DOI: 10.1142/s1793525324500031
Takeshi Isobe
{"title":"Morse homology for perturbed Dirac-harmonic maps into flat tori","authors":"Takeshi Isobe","doi":"10.1142/s1793525324500031","DOIUrl":"https://doi.org/10.1142/s1793525324500031","url":null,"abstract":"","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":"74 6","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139450440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Bounding the Lagrangian Hofer metric via barcodes 通过条形码限定拉格朗日霍费尔度量
IF 0.8 3区 数学
Journal of Topology and Analysis Pub Date : 2024-01-05 DOI: 10.1142/s1793525324500067
Patricia Dietzsch
{"title":"Bounding the Lagrangian Hofer metric via barcodes","authors":"Patricia Dietzsch","doi":"10.1142/s1793525324500067","DOIUrl":"https://doi.org/10.1142/s1793525324500067","url":null,"abstract":"","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":"20 6","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139450049","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Canonical nilpotent structure under bounded Ricci curvature and Reifenberg local covering geometry over regular limits 有界里奇曲率下的典型零点结构和规则极限上的雷芬伯格局部覆盖几何
IF 0.8 3区 数学
Journal of Topology and Analysis Pub Date : 2023-12-28 DOI: 10.1142/s1793525323500607
Zuohai Jiang, Lingling Kong, Shicheng Xu
{"title":"Canonical nilpotent structure under bounded Ricci curvature and Reifenberg local covering geometry over regular limits","authors":"Zuohai Jiang, Lingling Kong, Shicheng Xu","doi":"10.1142/s1793525323500607","DOIUrl":"https://doi.org/10.1142/s1793525323500607","url":null,"abstract":"<p>It is known that a closed collapsed Riemannian <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>n</mi></math></span><span></span>-manifold <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo stretchy=\"false\">)</mo></math></span><span></span> of bounded Ricci curvature and Reifenberg local covering geometry admits a nilpotent structure in the sense of Cheeger–Fukaya–Gromov with respect to a smoothed metric <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>g</mi><mo stretchy=\"false\">(</mo><mi>t</mi><mo stretchy=\"false\">)</mo></math></span><span></span>. We study the nilpotent structures over a regular limit space with optimal regularities that describe the collapsing of original metric <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>g</mi></math></span><span></span>, and prove that they are uniquely determined up to a conjugation by diffeomorphisms with bi-Lipschitz constant almost <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mn>1</mn></math></span><span></span>, and are equivalent to nilpotent structures arising from other nearby metrics <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>g</mi></mrow><mrow><mi>𝜖</mi></mrow></msub></math></span><span></span> with respect to <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>g</mi></mrow><mrow><mi>𝜖</mi></mrow></msub></math></span><span></span>’s sectional curvature bound.</p>","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":"9 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140173042","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 formality of the isotropy action on (ℤ2 ⊕ ℤ2)-symmetric spaces (ℤ2 ⊕ ℤ2)对称空间上各向同性作用的等变形式性
IF 0.8 3区 数学
Journal of Topology and Analysis Pub Date : 2023-12-14 DOI: 10.1142/s1793525323500504
Manuel Amann, Andreas Kollross
{"title":"Equivariant formality of the isotropy action on (ℤ2 ⊕ ℤ2)-symmetric spaces","authors":"Manuel Amann, Andreas Kollross","doi":"10.1142/s1793525323500504","DOIUrl":"https://doi.org/10.1142/s1793525323500504","url":null,"abstract":"<p>Compact symmetric spaces are probably one of the most prominent class of <i>formal</i> spaces, i.e. of spaces where the rational homotopy type is a formal consequence of the rational cohomology algebra. As a generalization, it is even known that their isotropy action is equivariantly formal. In this paper, we show that <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><msub><mrow><mi>ℤ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo stretchy=\"false\">⊕</mo><msub><mrow><mi>ℤ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo stretchy=\"false\">)</mo></math></span><span></span>-symmetric spaces are equivariantly formal and formal in the sense of Sullivan, in particular. Moreover, we give a short alternative proof of equivariant formality in the case of symmetric spaces with our new approach.</p>","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140168961","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Energy estimates of Yang—Mills functional 杨-米尔斯函数的能量估计
IF 0.8 3区 数学
Journal of Topology and Analysis Pub Date : 2023-11-23 DOI: 10.1142/s1793525323500619
Teng Huang
{"title":"Energy estimates of Yang—Mills functional","authors":"Teng Huang","doi":"10.1142/s1793525323500619","DOIUrl":"https://doi.org/10.1142/s1793525323500619","url":null,"abstract":"","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":"7 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139244743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Unitary connections on bratteli diagrams 布拉泰利图上的单元连接
IF 0.8 3区 数学
Journal of Topology and Analysis Pub Date : 2023-11-17 DOI: 10.1142/s1793525323500589
Paramita Das, Mainak Ghosh, S. Ghosh, Corey Jones
{"title":"Unitary connections on bratteli diagrams","authors":"Paramita Das, Mainak Ghosh, S. Ghosh, Corey Jones","doi":"10.1142/s1793525323500589","DOIUrl":"https://doi.org/10.1142/s1793525323500589","url":null,"abstract":"","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":"71 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139265418","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Resolution of singular fibers of an S1-manifold 解析 S1-manifold的奇异纤维
IF 0.8 3区 数学
Journal of Topology and Analysis Pub Date : 2023-11-15 DOI: 10.1142/s1793525323500565
Yi-Sheng Wang
{"title":"Resolution of singular fibers of an S1-manifold","authors":"Yi-Sheng Wang","doi":"10.1142/s1793525323500565","DOIUrl":"https://doi.org/10.1142/s1793525323500565","url":null,"abstract":"","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":"24 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139274090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Growth rate of dehn twist lattice points in teichmuller space teichmuller空间中dehn捻格点的生长速率
3区 数学
Journal of Topology and Analysis Pub Date : 2023-11-15 DOI: 10.1142/s179352532350053x
Jiawei Han
{"title":"Growth rate of dehn twist lattice points in teichmuller space","authors":"Jiawei Han","doi":"10.1142/s179352532350053x","DOIUrl":"https://doi.org/10.1142/s179352532350053x","url":null,"abstract":"Athreya, Bufetov, Eskin and Mirzakhani have shown the number of mapping class group lattice points intersecting a closed ball of radius $R$ in Teichm\"{u}ller space is asymptotic to $e^{hR}$, where $h$ is the dimension of the Teichm\"{u}ller space. In contrast we show the number of Dehn twist lattice points intersecting a closed ball of radius $R$ is coarsely asymptotic to $e^{frac{h}{2}R}$. Moreover, we show the number multi-twist lattice points intersecting a closed ball of radius $R$ grows coarsely at least at the rate of $R cdot e^{frac{h}{2}R}$.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":"10 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136227553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 1
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