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Relative Khovanov–Jacobsson classes 相对khovanov - jacobson类
IF 0.7 3区 数学
Algebraic and Geometric Topology Pub Date : 2021-03-02 DOI: 10.2140/agt.2022.22.3983
I. Sundberg, Jonah Swann
{"title":"Relative Khovanov–Jacobsson classes","authors":"I. Sundberg, Jonah Swann","doi":"10.2140/agt.2022.22.3983","DOIUrl":"https://doi.org/10.2140/agt.2022.22.3983","url":null,"abstract":"To a smooth, compact, oriented, properly-embedded surface in the $4$-ball, we define an invariant of its boundary-preserving isotopy class from the Khovanov homology of its boundary link. Previous work showed that when the boundary link is empty, this invariant is determined by the genus of the surface. We show that this relative invariant: can obstruct sliceness of knots; detects a pair of slices for $9_{46}$; is not hindered by detecting connected sums with knotted $2$-spheres.","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"115 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79457676","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: 9
Homology of even Artin kernels 偶丁核的同源性
IF 0.7 3区 数学
Algebraic and Geometric Topology Pub Date : 2021-02-23 DOI: 10.2140/agt.2022.22.349
Rub'en Blasco-Garc'ia, J. I. Cogolludo-Agust'in, Conchita Mart'inez-P'erez
{"title":"Homology of even Artin kernels","authors":"Rub'en Blasco-Garc'ia, J. I. Cogolludo-Agust'in, Conchita Mart'inez-P'erez","doi":"10.2140/agt.2022.22.349","DOIUrl":"https://doi.org/10.2140/agt.2022.22.349","url":null,"abstract":". We explicitly compute the homology groups with coefficients in a field of characteristic zero of cocyclic subgroups or even Artin groups of FC-type. We also give some partial results in the case when the coefficients are taken in a field of prime characteristic.","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"19 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72490294","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
On finitely generated normal subgroups ofKähler groups 在有限生成的正常子群ofKähler群上
IF 0.7 3区 数学
Algebraic and Geometric Topology Pub Date : 2021-02-01 DOI: 10.2140/agt.2022.22.2997
Francisco Nicol'as
{"title":"On finitely generated normal subgroups of\u0000Kähler groups","authors":"Francisco Nicol'as","doi":"10.2140/agt.2022.22.2997","DOIUrl":"https://doi.org/10.2140/agt.2022.22.2997","url":null,"abstract":"We prove that if a surface group embeds as a normal subgroup in a K¨ahler group and the conjugation action of the K¨ahler group on the surface group preserves the conjugacy class of a non-trivial element, then the K¨ahler group is virtually given by a direct product, where one factor is a surface group. Moreover we prove that if a one-ended hyperbolic group with infinite outer automorphism group embeds as a normal subgroup in a K¨ahler group then it is virtually a surface group. More generally we give restrictions on normal subgroups of K¨ahler groups which are amalgamated products or HNN extensions.","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"17 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88302235","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
Golod and tight 3–manifolds 良好和紧密的3 -歧管
IF 0.7 3区 数学
Algebraic and Geometric Topology Pub Date : 2021-01-30 DOI: 10.2140/agt.2023.23.2191
Kouyemon Iriye, D. Kishimoto
{"title":"Golod and tight 3–manifolds","authors":"Kouyemon Iriye, D. Kishimoto","doi":"10.2140/agt.2023.23.2191","DOIUrl":"https://doi.org/10.2140/agt.2023.23.2191","url":null,"abstract":"The notions Golodness and tightness for simplicial complexes come from algebra and geometry, respectively. We prove these two notions are equivalent for 3-manifold triangulations, through a topological characterization of a polyhedral product for a tight-neighborly manifold triangulation of dimension $ge 3$.","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"36 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82874850","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
Maximal knotless graphs 最大无结图
IF 0.7 3区 数学
Algebraic and Geometric Topology Pub Date : 2021-01-13 DOI: 10.2140/agt.2023.23.1831
L. Eakins, Thomas Fleming, T. Mattman
{"title":"Maximal knotless graphs","authors":"L. Eakins, Thomas Fleming, T. Mattman","doi":"10.2140/agt.2023.23.1831","DOIUrl":"https://doi.org/10.2140/agt.2023.23.1831","url":null,"abstract":"A graph is maximal knotless if it is edge maximal for the property of knotless embedding in $R^3$. We show that such a graph has at least $frac74 |V|$ edges, and construct an infinite family of maximal knotless graphs with $|E|<frac52|V|$. With the exception of $|E| = 22$, we show that for any $|E| geq 20$ there exists a maximal knotless graph of size $|E|$. We classify the maximal knotless graphs through nine vertices and 20 edges. We determine which of these maxnik graphs are the clique sum of smaller graphs and construct an infinite family of maxnik graphs that are not clique sums.","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"3 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88235075","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
Quasi-isometric rigidity of subgroups and filtered ends 子群和过滤端的准等距刚性
IF 0.7 3区 数学
Algebraic and Geometric Topology Pub Date : 2020-12-18 DOI: 10.2140/agt.2022.22.3023
Eduardo Mart'inez-Pedroza, Luis Jorge S'anchez Saldana
{"title":"Quasi-isometric rigidity of subgroups and filtered ends","authors":"Eduardo Mart'inez-Pedroza, Luis Jorge S'anchez Saldana","doi":"10.2140/agt.2022.22.3023","DOIUrl":"https://doi.org/10.2140/agt.2022.22.3023","url":null,"abstract":"Let $G$ and $H$ be quasi-isometric finitely generated groups and let $Pleq G$; is there a subgroup $Q$ (or a collection of subgroups) of $H$ whose left cosets coarsely reflect the geometry of the left cosets of $P$ in $G$? We explore sufficient conditions for a positive answer. The article consider pairs of the form $(G,mathcal{P})$ where $G$ is a finitely generated group and $mathcal{P}$ a finite collection of subgroups, there is a notion of quasi-isometry of pairs, and quasi-isometrically characteristic collection of subgroups. A subgroup is qi-characteristic if it belongs to a qi-characteristic collection. Distinct classes of qi-characteristic collections of subgroups have been studied in the literature on quasi-isometric rigidity, we list in the article some of them and provide other examples. The first part of the article proves: if $G$ and $H$ are finitely generated quasi-isometric groups and $mathcal{P}$ is a qi-characteristic collection of subgroups of $G$, then there is a collection of subgroups $mathcal{Q}$ of $H$ such that $ (G, mathcal{P})$ and $(H, mathcal{Q})$ are quasi-isometric pairs. The second part of the article studies the number of filtered ends $tilde e (G, P)$ of a pair of groups, a notion introduced by Bowditch, and provides an application of our main result: if $G$ and $H$ are quasi-isometric groups and $Pleq G$ is qi-characterstic, then there is $Qleq H$ such that $tilde e (G, P) = tilde e (H, Q)$.","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"128 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83971741","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: 4
Unexpected essential surfaces among exteriors of twisted torus knots 意想不到的基本表面在扭曲的环状结的外部之间
IF 0.7 3区 数学
Algebraic and Geometric Topology Pub Date : 2020-12-17 DOI: 10.2140/agt.2022.22.3965
Thiago de Paiva
{"title":"Unexpected essential surfaces among exteriors of twisted torus knots","authors":"Thiago de Paiva","doi":"10.2140/agt.2022.22.3965","DOIUrl":"https://doi.org/10.2140/agt.2022.22.3965","url":null,"abstract":"The twisted torus knots K(p, q; r, s) are obtained by performing a sequence of s full twists on r adjacent strands of (p, q)-torus knots. In this paper, we answer two questions related to essential surfaces in the exteriors of twisted torus knots. Namely, we show there are prime numbers r greater than 2 such that K(p, q; r, s) contain closed essential surface in their exterior, answering a question of Morimoto and Yamada. Additionally, Morimoto asked whether all twisted torus knots with essential tori in the exterior fit into one of two families. We find a new infinite family that was previously unknown.","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"14 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77352572","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: 8
A quantum invariant of links in T2× I withvolume conjecture behavior 具有体积猜想行为的t2xi中链路的量子不变量
IF 0.7 3区 数学
Algebraic and Geometric Topology Pub Date : 2020-12-14 DOI: 10.2140/agt.2023.23.1891
Joseph Boninger
{"title":"A quantum invariant of links in T2× I with\u0000volume conjecture behavior","authors":"Joseph Boninger","doi":"10.2140/agt.2023.23.1891","DOIUrl":"https://doi.org/10.2140/agt.2023.23.1891","url":null,"abstract":"We define a polynomial invariant $J_n^T$ of links in the thickened torus. We call $J^T_n$ the $n$th toroidal colored Jones polynomial, and show it satisfies many properties of the original colored Jones polynomial. Most significantly, $J_n^T$ exhibits volume conjecture behavior. We prove the volume conjecture for the 2-by-2 square weave, and provide computational evidence for other links. We also give two equivalent constructions of $J_n^T,$ one using operator invariants and another using the Kauffman bracket skein module of the torus. In the process we generalize the theory of operator invariants to links in $T^2 times I$, defining what we call a pseudo-operator invariant.","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"27 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90962289","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
Finite presentations for stated skein algebras and lattice gauge field theory 陈述绞结代数的有限表示与点阵规范场论
IF 0.7 3区 数学
Algebraic and Geometric Topology Pub Date : 2020-12-06 DOI: 10.2140/agt.2023.23.1249
J. Korinman
{"title":"Finite presentations for stated skein algebras and lattice gauge field theory","authors":"J. Korinman","doi":"10.2140/agt.2023.23.1249","DOIUrl":"https://doi.org/10.2140/agt.2023.23.1249","url":null,"abstract":"We provide finite presentations for stated skein algebras and deduce that those algebras are Koszul and that they are isomorphic to the quantum moduli algebras appearing in lattice gauge field theory, generalizing previous results of Bullock, Frohman, Kania-Bartoszynska and Faitg.","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"61 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84765190","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: 9
Most big mapping class groups fail the Tits alternative 大多数大型映射类组都不能使用Tits
IF 0.7 3区 数学
Algebraic and Geometric Topology Pub Date : 2020-12-02 DOI: 10.2140/agt.2021.21.3675
Daniel Allcock
{"title":"Most big mapping class groups fail the Tits alternative","authors":"Daniel Allcock","doi":"10.2140/agt.2021.21.3675","DOIUrl":"https://doi.org/10.2140/agt.2021.21.3675","url":null,"abstract":"Let $X$ be a surface, possibly with boundary. Suppose it has infinite genus or infinitely many punctures, or a closed subset which is a disk with a Cantor set removed from its interior. For example, $X$ could be any surface of infinite type with only finitely many boundary components. We prove that the mapping class group of $X$ does not satisfy the Tits Alternative. That is, Map$(X)$ contains a finitely generated subgroup that is not virtually solvable and contains no nonabelian free group.","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"2 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80904413","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
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