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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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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
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":null,"pages":null},"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
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":null,"pages":null},"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
Real polynomials with constrained real divisors. i. fundamental groups 带约束实因子的实多项式。一、基本群
3区 数学
Journal of Topology and Analysis Pub Date : 2023-11-15 DOI: 10.1142/s1793525323500553
Gabriel Katz, Boris Shapiro, Volkmar Welker
{"title":"Real polynomials with constrained real divisors. i. fundamental groups","authors":"Gabriel Katz, Boris Shapiro, Volkmar Welker","doi":"10.1142/s1793525323500553","DOIUrl":"https://doi.org/10.1142/s1793525323500553","url":null,"abstract":"In the late 80s, V.~Arnold and V.~Vassiliev initiated the topological study of the space of real univariate polynomials of a given degree d and with no real roots of multiplicity exceeding a given positive integer. Expanding their studies, we consider the spaces of real monic univariate polynomials of degree d whose real divisors avoid sequences of root multiplicities taken from a given poset of compositions which is closed under certain natural combinatorial operations. In this paper, we concentrate on the fundamental group of such spaces. We find explicit presentations for the fundamental groups in terms of generators and relations and show that in a number of cases they are free with rank bounded from above by a quadratic function in d. We also show that the fundamental group stabilizes for d large. We further show that the fundamental groups admit an interpretation as special bordisms of immersions of 1-manifolds into the cylinder S^1 times R, whose images avoid the tangency patterns from the poset with respect to the generators of the cylinder.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136227551","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: 3
General primitivity in the mapping class group 映射类组中的一般原语
3区 数学
Journal of Topology and Analysis Pub Date : 2023-11-15 DOI: 10.1142/s1793525323500541
Pankaj Kapari, Kashyap Rajeevsarathy
{"title":"General primitivity in the mapping class group","authors":"Pankaj Kapari, Kashyap Rajeevsarathy","doi":"10.1142/s1793525323500541","DOIUrl":"https://doi.org/10.1142/s1793525323500541","url":null,"abstract":"For $ggeq 2$, let $text{Mod}(S_g)$ be the mapping class group of the closed orientable surface $S_g$ of genus $g$. In this paper, we obtain necessary and sufficient conditions under which a given pseudo-periodic mapping can be a root of another up to conjugacy. Using this characterization, the canonical decomposition of (non-periodic) mapping classes, and some known algorithms, we give a theoretical algorithm for computing its roots up to conjugacy. Furthermore, we derive realizable bounds on the degrees of roots of pseudo-periodic mapping classes in $text{Mod}(S_g)$, the Torelli group, the level-$m$ subgroup of $text{Mod}(S_g)$, and the commutator subgroup of $text{Mod}(S_2)$. In particular, we show that the highest possible (realizable) degree of a root of a pseudo-periodic mapping class $F$ is $3q(F)(g+1)(g+2)$, realized by the roots of $T_c^{q(F)}$, where $c$ is a separating curve in $S_g$ of genus $[g/2]$ and $q(F)$ is a unique positive integer associated with the conjugacy class of $F$. Finally, for $ggeq 3$ we show that any pseudo-periodic having a nontrivial periodic component that is not the hyperelliptic involution, normally generates $text{Mod}(S_g)$. Consequently, we establish there always exist roots of bounding pair maps and powers of Dehn twists that normally generate $text{Mod}(S_g)$.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136227558","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: 2
Tomiyama's K-commutative diagrams of minimal dynamical systems 富山最小动力系统的 K-commutative 图
IF 0.8 3区 数学
Journal of Topology and Analysis Pub Date : 2023-11-15 DOI: 10.1142/s1793525323500498
Sihan Wei
{"title":"Tomiyama's K-commutative diagrams of minimal dynamical systems","authors":"Sihan Wei","doi":"10.1142/s1793525323500498","DOIUrl":"https://doi.org/10.1142/s1793525323500498","url":null,"abstract":"","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139273905","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
Reducing spheres of genus-2 Heegaard splitting of S3 S3 的 2 属 Heegaard 分裂的还原球
IF 0.8 3区 数学
Journal of Topology and Analysis Pub Date : 2023-11-15 DOI: 10.1142/s1793525323500462
Sreekrishna Palaparthi, Swapnendu Panda
{"title":"Reducing spheres of genus-2 Heegaard splitting of S3","authors":"Sreekrishna Palaparthi, Swapnendu Panda","doi":"10.1142/s1793525323500462","DOIUrl":"https://doi.org/10.1142/s1793525323500462","url":null,"abstract":"","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139271245","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
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