Pub Date : 2023-11-15DOI: 10.1142/s1793525323500528
Hongbin Sun, Zhongzi Wang
{"title":"Maps from 3-manifolds to 4-manifolds that induce isomorphisms on π1","authors":"Hongbin Sun, Zhongzi Wang","doi":"10.1142/s1793525323500528","DOIUrl":"https://doi.org/10.1142/s1793525323500528","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":"139276145","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}
Pub Date : 2023-11-15DOI: 10.1142/s1793525323500474
Hyungryul Baik, Dongryul M. Kim, Chenxi Wu
{"title":"Reducible normal generators for mapping class groups are abundant","authors":"Hyungryul Baik, Dongryul M. Kim, Chenxi Wu","doi":"10.1142/s1793525323500474","DOIUrl":"https://doi.org/10.1142/s1793525323500474","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":"139271090","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}
Pub Date : 2023-11-15DOI: 10.1142/s1793525323500486
Regina Rotman
It is not known whether or not the lenth of the shortest periodic geodesic on a closed Riemannian manifold $M^n$ can be majorized by $c(n) vol^{ 1 over n}$, or $tilde{c}(n)d$, where $n$ is the dimension of $M^n$, $vol$ denotes the volume of $M^n$, and $d$ denotes its diameter. In this paper we will prove that for each $epsilon >0$ one can find such estimates for the length of a geodesic loop with with angle between $pi-epsilon$ and $pi$ with an explicit constant that depends both on $n$ and $epsilon$. That is, let $epsilon > 0$, and let $a = lceil{ {1 over {sin ({epsilon over 2})}}} rceil+1 $. We will prove that there exists a wide (i.e. with an angle that is wider than $pi-epsilon$) geodesic loop on $M^n$ of length at most $2n!a^nd$. We will also show that there exists a wide geodesic loop of length at most $2(n+1)!^2a^{(n+1)^3} FillRad leq 2 cdot n(n+1)!^2a^{(n+1)^3} vol^{1 over n}$. Here $FillRad$ is the Filling Radius of $M^n$.
目前尚不清楚闭合黎曼流形$M^n$上最短周期测地线的长度是否可以用$c(n) vol^{ 1 over n}$或$tilde{c}(n)d$来表示，其中$n$是$M^n$的尺寸，$vol$表示$M^n$的体积，$d$表示其直径。在本文中，我们将证明，对于每一个$epsilon >0$，我们都可以找到这样的测量回路长度的估计，其角度在$pi-epsilon$和$pi$之间，并具有一个显式常数，该常数依赖于$n$和$epsilon$。也就是说，设$epsilon > 0$，设$a = lceil{ {1 over {sin ({epsilon over 2})}}} rceil+1 $。我们将证明在$M^n$上存在一个长度不超过$2n!a^nd$的宽(即夹角大于$pi-epsilon$)测地线环。我们还将证明存在长度最多为$2(n+1)!^2a^{(n+1)^3} FillRad leq 2 cdot n(n+1)!^2a^{(n+1)^3} vol^{1 over n}$的宽测地线回路。其中$FillRad$为$M^n$的填充半径。
{"title":"Wide short geodesic loops on closed Riemannian manifolds","authors":"Regina Rotman","doi":"10.1142/s1793525323500486","DOIUrl":"https://doi.org/10.1142/s1793525323500486","url":null,"abstract":"It is not known whether or not the lenth of the shortest periodic geodesic on a closed Riemannian manifold $M^n$ can be majorized by $c(n) vol^{ 1 over n}$, or $tilde{c}(n)d$, where $n$ is the dimension of $M^n$, $vol$ denotes the volume of $M^n$, and $d$ denotes its diameter. In this paper we will prove that for each $epsilon >0$ one can find such estimates for the length of a geodesic loop with with angle between $pi-epsilon$ and $pi$ with an explicit constant that depends both on $n$ and $epsilon$. That is, let $epsilon > 0$, and let $a = lceil{ {1 over {sin ({epsilon over 2})}}} rceil+1 $. We will prove that there exists a wide (i.e. with an angle that is wider than $pi-epsilon$) geodesic loop on $M^n$ of length at most $2n!a^nd$. We will also show that there exists a wide geodesic loop of length at most $2(n+1)!^2a^{(n+1)^3} FillRad leq 2 cdot n(n+1)!^2a^{(n+1)^3} vol^{1 over n}$. Here $FillRad$ is the Filling Radius of $M^n$.","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":"136227754","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}
Pub Date : 2023-11-15DOI: 10.1142/s1793525323500577
Olga Frolkina
{"title":"New examples in dimensions N ≥ 4 related to a question of J.W. Cannon and S.G. Wayment","authors":"Olga Frolkina","doi":"10.1142/s1793525323500577","DOIUrl":"https://doi.org/10.1142/s1793525323500577","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":"139271130","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}
Pub Date : 2023-11-10DOI: 10.1142/s1793525323500413
Benedikt Hunger
Almost flat finitely generated projective Hilbert C*-module bundles were successfully used by Hanke and Schick to prove special cases of the Strong Novikov Conjecture. Dadarlat later showed that it is possible to calculate the index of a K-homology class $etain K_*(M)$ twisted with an almost flat bundle in terms of the image of $eta$ under Lafforgue's assembly map and the almost representation associated to the bundle. Mishchenko used flat infinite-dimensional bundles equipped with a Fredholm operator in order to prove special cases of the Novikov higher signature conjecture.
{"title":"Asymptotically Flat Fredholm Bundles and Assembly","authors":"Benedikt Hunger","doi":"10.1142/s1793525323500413","DOIUrl":"https://doi.org/10.1142/s1793525323500413","url":null,"abstract":"Almost flat finitely generated projective Hilbert C*-module bundles were successfully used by Hanke and Schick to prove special cases of the Strong Novikov Conjecture. Dadarlat later showed that it is possible to calculate the index of a K-homology class $etain K_*(M)$ twisted with an almost flat bundle in terms of the image of $eta$ under Lafforgue's assembly map and the almost representation associated to the bundle. Mishchenko used flat infinite-dimensional bundles equipped with a Fredholm operator in order to prove special cases of the Novikov higher signature conjecture. ","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135087571","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}
Pub Date : 2023-11-10DOI: 10.1142/s1793525323500383
Susumu Hirose, Genki Omori
{"title":"Finite Presentations for the Balanced Superelliptic Mapping Class Groups","authors":"Susumu Hirose, Genki Omori","doi":"10.1142/s1793525323500383","DOIUrl":"https://doi.org/10.1142/s1793525323500383","url":null,"abstract":"","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135186914","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}
Pub Date : 2023-11-10DOI: 10.1142/s1793525323500437
Maria Simkova
This paper proposes an algorithm that decides if two simply connected spaces represented by finite simplicial sets of finite $k$-type and finite dimension $d$ are homotopy equivalent. If the spaces are homotopy equivalent, the algorithm finds a homotopy equivalence between their Postnikov stages in dimension $d$. As a consequence, we get an algorithm deciding if two spaces represented by finite simplicial sets are stably homotopy equivalent.
{"title":"Are two <i>H</i>-Spaces Homotopy Equivalent? An Algorithmic View Point","authors":"Maria Simkova","doi":"10.1142/s1793525323500437","DOIUrl":"https://doi.org/10.1142/s1793525323500437","url":null,"abstract":"This paper proposes an algorithm that decides if two simply connected spaces represented by finite simplicial sets of finite $k$-type and finite dimension $d$ are homotopy equivalent. If the spaces are homotopy equivalent, the algorithm finds a homotopy equivalence between their Postnikov stages in dimension $d$. As a consequence, we get an algorithm deciding if two spaces represented by finite simplicial sets are stably homotopy equivalent.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135186911","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}
Pub Date : 2023-11-10DOI: 10.1142/s1793525323500371
Michael Gene Dobbins
We study the evolution of a Jordan curve on the 2-sphere by curvature flow, also known as curve shortening flow, and by level-set flow, which is a weak formulation of curvature flow. We show that the evolution of the curve depends continuously on the initial curve in Frechet distance in the case where the curve bisects the sphere. This even holds in the limit as time goes to infinity. This builds on Joseph Lauer's work on existence and uniqueness of solutions to the curvature flow problem on the sphere when the initial curve is not smooth.
{"title":"Continuous dependence of curvature flow on initial conditions","authors":"Michael Gene Dobbins","doi":"10.1142/s1793525323500371","DOIUrl":"https://doi.org/10.1142/s1793525323500371","url":null,"abstract":"We study the evolution of a Jordan curve on the 2-sphere by curvature flow, also known as curve shortening flow, and by level-set flow, which is a weak formulation of curvature flow. We show that the evolution of the curve depends continuously on the initial curve in Frechet distance in the case where the curve bisects the sphere. This even holds in the limit as time goes to infinity. This builds on Joseph Lauer's work on existence and uniqueness of solutions to the curvature flow problem on the sphere when the initial curve is not smooth.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135087723","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}
Pub Date : 2023-11-10DOI: 10.1142/s1793525323500425
Bruno Staffa
Stationary geodesic networks are the analogs of closed geodesics whose domain is a graph instead of a circle. We prove that for a generic Riemannian metric on a smooth manifold $M$ regular stationary geodesic nets are non-degenerate.
{"title":"Bumpy Metrics Theorem for Geodesic Nets","authors":"Bruno Staffa","doi":"10.1142/s1793525323500425","DOIUrl":"https://doi.org/10.1142/s1793525323500425","url":null,"abstract":"Stationary geodesic networks are the analogs of closed geodesics whose domain is a graph instead of a circle. We prove that for a generic Riemannian metric on a smooth manifold $M$ regular stationary geodesic nets are non-degenerate.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135087572","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}
Pub Date : 2023-11-10DOI: 10.1142/s1793525323500449
Genki Omori, Yuya Yoshida
The balanced superelliptic handlebody group is the normalizer of the transformation group of the balanced superelliptic covering space in the handlebody group of the total space. We give a finite presentation for the balanced superelliptic handlebody group. To give this presentation, we construct a finite presentation for the liftable Hilden group.
{"title":"A Finite Presentation for the Balanced Superelliptic Handlebody Group","authors":"Genki Omori, Yuya Yoshida","doi":"10.1142/s1793525323500449","DOIUrl":"https://doi.org/10.1142/s1793525323500449","url":null,"abstract":"The balanced superelliptic handlebody group is the normalizer of the transformation group of the balanced superelliptic covering space in the handlebody group of the total space. We give a finite presentation for the balanced superelliptic handlebody group. To give this presentation, we construct a finite presentation for the liftable Hilden group.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135186912","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}
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