{"title":"Exotic Dehn twists and homotopy coherent group actions","authors":"Sungkyung Kang, JungHwan Park, Masaki Taniguchi","doi":"arxiv-2409.11806","DOIUrl":"https://doi.org/arxiv-2409.11806","url":null,"abstract":"We consider the question of extending a smooth homotopy coherent finite\u0000cyclic group action on the boundary of a smooth 4-manifold to its interior. As\u0000a result, we prove that Dehn twists along any Seifert homology sphere, except\u0000the 3-sphere, on their simply connected positive-definite fillings are infinite\u0000order exotic.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256729","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"$infty$-operadic foundations for embedding calculus","authors":"Manuel Krannich, Alexander Kupers","doi":"arxiv-2409.10991","DOIUrl":"https://doi.org/arxiv-2409.10991","url":null,"abstract":"Motivated by applications to spaces of embeddings and automorphisms of\u0000manifolds, we consider a tower of $infty$-categories of truncated\u0000right-modules over a unital $infty$-operad $mathcal{O}$. We study monoidality\u0000and naturality properties of this tower, identify its layers, describe the\u0000difference between the towers as $mathcal{O}$ varies, and generalise these\u0000results to the level of Morita $(infty,2)$-categories. Applied to the ${rm\u0000BO}(d)$-framed $E_d$-operad, this extends Goodwillie-Weiss' embedding calculus\u0000and its layer identification to the level of bordism categories. Applied to\u0000other variants of the $E_d$-operad, it yields new versions of embedding\u0000calculus, such as one for topological embeddings, based on ${rm BTop}(d)$, or\u0000one similar to Boavida de Brito-Weiss' configuration categories, based on ${rm\u0000BAut}(E_d)$. In addition, we prove a delooping result in the context of\u0000embedding calculus, establish a convergence result for topological embedding\u0000calculus, improve upon the smooth convergence result of Goodwillie, Klein, and\u0000Weiss, and deduce an Alexander trick for homology 4-spheres.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256730","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Classification of horocycle orbit closures in $ mathbb{Z} $-covers","authors":"James Farre, Or Landesberg, Yair Minsky","doi":"arxiv-2409.10004","DOIUrl":"https://doi.org/arxiv-2409.10004","url":null,"abstract":"We fully describe all horocycle orbit closures in $ mathbb{Z} $-covers of\u0000compact hyperbolic surfaces. Our results rely on a careful analysis of the\u0000efficiency of all distance minimizing geodesic rays in the cover. As a\u0000corollary we obtain in this setting that all non-maximal horocycle orbit\u0000closures, while fractal, have integer Hausdorff dimension.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A note on lattice knots","authors":"Sasha Anan'in, Alexandre Grishkov, Dmitrii Korshunov","doi":"arxiv-2409.10691","DOIUrl":"https://doi.org/arxiv-2409.10691","url":null,"abstract":"The aim of this note is to share the observation that the set of elementary\u0000operations of Turing on lattice knots can be reduced to just one type of simple\u0000local switches.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256732","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Pressure path metrics on parabolic families of polynomials","authors":"Fabrizio Bianchi, Yan Mary He","doi":"arxiv-2409.10462","DOIUrl":"https://doi.org/arxiv-2409.10462","url":null,"abstract":"Let $Lambda$ be a subfamily of the moduli space of degree $Dge2$\u0000polynomials defined by a finite number of parabolic relations. Let $Omega$ be\u0000a bounded stable component of $Lambda$ with the property that all critical\u0000points are attracted by either the persistent parabolic cycles or by attracting\u0000cycles in $mathbb C$. We construct a positive semi-definite pressure form on\u0000$Omega$ and show that it defines a path metric on $Omega$. This provides a\u0000counterpart in complex dynamics of the pressure metric on cusped Hitchin\u0000components recently studied by Kao and Bray-Canary-Kao-Martone.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"194 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Simultaneous Uniformization and Algebraic Correspondences","authors":"Mahan Mj, Sabyasachi Mukherjee","doi":"arxiv-2409.10468","DOIUrl":"https://doi.org/arxiv-2409.10468","url":null,"abstract":"We prove a generalization of the Bers' simultaneous uniformization theorem in\u0000the world of algebraic correspondences. More precisely, we construct algebraic\u0000correspondences that simultaneously uniformize a pair of non-homeomorphic genus\u0000zero orbifolds. We also present a complex-analytic realization of the\u0000Teichm\"uller space of a punctured sphere in the space of correspondences.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"202 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Enhanced Hantzsche Theorem","authors":"Michael H. Freedman","doi":"arxiv-2409.09983","DOIUrl":"https://doi.org/arxiv-2409.09983","url":null,"abstract":"A closed 3-manifold $M$ may be described up to some indeterminacy by a\u0000Heegaard diagram $mathcal{D}$. The question \"Does $M$ smoothly embed in\u0000$mathbb{R}^4$?'' is equivalent to a property of $mathcal{D}$ which we call\u0000$textit{doubly unlinked}$ (DU). This perspective leads to an enhancement of\u0000Hantzsche's embedding obstruction.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The horocyclic metric on Teichm{ü}ller spaces","authors":"Hideki MiyachiIRMA, Ken'Ichi OhshikaIRMA, Athanase PapadopoulosIRMA","doi":"arxiv-2409.10082","DOIUrl":"https://doi.org/arxiv-2409.10082","url":null,"abstract":"In his paper Minimal stretch maps between hyperbolic surfaces, William\u0000Thurston defined a norm on the tangent space to Teichm{\"u}ller space of a\u0000hyperbolic surface, which he called the earthquake norm. This norm is obtained\u0000by assigning a length to a tangent vector after such a vector is considered as\u0000an infinitesimal earthquake deformation of the surface. This induces a Finsler\u0000metric on the Teichm{\"u}ller space, called the earthquake metric. This theory\u0000was recently investigated by Huang, Ohshika, Pan and Papadopoulos. In the\u0000present paper, we study this metric from the conformal viewpoint and we adapt\u0000Thurston's theory to the case of Riemann surfaces of arbitrary genus with\u0000marked points. A complex version of the Legendre transform defined for Finsler\u0000manifolds gives an analogue of the Wolpert duality for the Weil-Petersson\u0000symplectic form, which establishes a complete analogue of Thurston's theory of\u0000the earthquake norm in the conformal setting.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Two curious strongly invertible L-space knots","authors":"Kenneth L. Baker, Marc Kegel, Duncan McCoy","doi":"arxiv-2409.09833","DOIUrl":"https://doi.org/arxiv-2409.09833","url":null,"abstract":"We present two examples of strongly invertible L-space knots whose surgeries\u0000are never the double branched cover of a Khovanov thin link in the 3-sphere.\u0000Consequently, these knots provide counterexamples to a conjectural\u0000characterization of strongly invertible L-space knots due to Watson. We also\u0000discuss other exceptional properties of these two knots, for example, these two\u0000L-space knots have formal semigroups that are actual semigroups.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256735","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The search for alternating surgeries","authors":"Kenneth L. Baker, Marc Kegel, Duncan McCoy","doi":"arxiv-2409.09842","DOIUrl":"https://doi.org/arxiv-2409.09842","url":null,"abstract":"Surgery on a knot in $S^3$ is said to be an alternating surgery if it yields\u0000the double branched cover of an alternating link. The main theoretical\u0000contribution is to show that the set of alternating surgery slopes is\u0000algorithmically computable and to establish several structural results.\u0000Furthermore, we calculate the set of alternating surgery slopes for many\u0000examples of knots, including all hyperbolic knots in the SnapPy census. These\u0000examples exhibit several interesting phenomena including strongly invertible\u0000knots with a unique alternating surgery and asymmetric knots with two\u0000alternating surgery slopes. We also establish upper bounds on the set of\u0000alternating surgeries, showing that an alternating surgery slope on a\u0000hyperbolic knot satisfies $|p/q| leq 3g(K)+4$. Notably, this bound applies to\u0000lens space surgeries, thereby strengthening the known genus bounds from the\u0000conjecture of Goda and Teragaito.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"58 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
