发布求助
文献互助 智能选刊 最新文献

arXiv - MATH - Geometric Topology最新文献

筛选
英文 中文
A determinant formula of the Jones polynomial for a family of braids 辫状线族的琼斯多项式行列式
arXiv - MATH - Geometric Topology Pub Date : 2024-08-23 DOI: arxiv-2408.13410
Derya Asaner, Sanjay Kumar, Melody Molander, Andrew Pease, Anup Poudel
{"title":"A determinant formula of the Jones polynomial for a family of braids","authors":"Derya Asaner, Sanjay Kumar, Melody Molander, Andrew Pease, Anup Poudel","doi":"arxiv-2408.13410","DOIUrl":"https://doi.org/arxiv-2408.13410","url":null,"abstract":"In 2012, Cohen, Dasbach, and Russell presented an algorithm to construct a\u0000weighted adjacency matrix for a given knot diagram. In the case of pretzel\u0000knots, it is shown that after evaluation, the determinant of the matrix\u0000recovers the Jones polynomial. Although the Jones polynomial is known to be\u0000#P-hard by Jaeger, Vertigan, and Welsh, this presents a class of knots for\u0000which the Jones polynomial can be computed in polynomial time by using the\u0000determinant. In this paper, we extend these results by recovering the Jones\u0000polynomial as the determinant of a weighted adjacency matrix for certain\u0000subfamilies of the braid group. Lastly, we compute the Kauffman polynomial of\u0000(2,q) torus knots in polynomial time using the balanced overlaid Tait graphs.\u0000This is the first known example of generalizing the methodology of Cohen to a\u0000class of quantum invariants which cannot be derived from the HOMFLYPT\u0000polynomial.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192254","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}
引用次数: 0
Rank-$N$ Dimer Models on Surfaces 表面上的 Rank-$N$ 二聚体模型
arXiv - MATH - Geometric Topology Pub Date : 2024-08-22 DOI: arxiv-2408.12066
Sri Tata
{"title":"Rank-$N$ Dimer Models on Surfaces","authors":"Sri Tata","doi":"arxiv-2408.12066","DOIUrl":"https://doi.org/arxiv-2408.12066","url":null,"abstract":"The web trace theorem of Douglas, Kenyon, Shi expands the twisted Kasteleyn\u0000determinant in terms of traces of webs. We generalize this theorem to higher\u0000genus surfaces and expand the twisted Kasteleyn matrices corresponding to spin\u0000structures on the surface, analogously to the rank-1 case of Cimasoni,\u0000Reshetikhin. In the process of the proof, we give an alternate geometric\u0000derivation of the planar web trace theorem, relying on the spin geometry of\u0000embedded loops and a `racetrack construction' used to immerse loops in the\u0000blowup graph on the surface.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"48 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192258","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}
引用次数: 0
Three-Dimensional Small Covers and Links 三维小封面和链接
arXiv - MATH - Geometric Topology Pub Date : 2024-08-22 DOI: arxiv-2408.12557
Vladimir Gorchakov
{"title":"Three-Dimensional Small Covers and Links","authors":"Vladimir Gorchakov","doi":"arxiv-2408.12557","DOIUrl":"https://doi.org/arxiv-2408.12557","url":null,"abstract":"We study certain orientation-preserving involutions on three-dimensional\u0000small covers. We prove that the quotient space of an orientable\u0000three-dimensional small cover by such an involution belonging to the 2-torus is\u0000homeomorphic to a connected sum of copies of $S^2 times S^1$. If this quotient\u0000space is a 3-sphere, then the corresponding small cover is a two-fold branched\u0000covering of the 3-sphere along a link. We provide a description of this link in\u0000terms of the polytope and the characteristic function.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"61 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192256","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}
引用次数: 0
On 2-complexes embeddable in 4-space, and the excluded minors of their underlying graphs 关于可嵌入 4 空间的 2 复数及其底层图的排除最小值
arXiv - MATH - Geometric Topology Pub Date : 2024-08-22 DOI: arxiv-2408.12681
Agelos Georgakopoulos, Martin Winter
{"title":"On 2-complexes embeddable in 4-space, and the excluded minors of their underlying graphs","authors":"Agelos Georgakopoulos, Martin Winter","doi":"arxiv-2408.12681","DOIUrl":"https://doi.org/arxiv-2408.12681","url":null,"abstract":"We study the potentially undecidable problem of whether a given 2-dimensional\u0000CW complex can be embedded into $mathbb{R}^4$. We provide operations that\u0000preserve embeddability, including joining and cloning of 2-cells, as well as\u0000$Deltamathrm Y$-transformations. We also construct a CW complex for which\u0000$mathrm YDelta$-transformations do not preserve embeddability. We use these results to study 4-flat graphs, i.e., graphs that embed in\u0000$mathbb{R}^4$ after attaching any number of 2-cells to their cycles; a graph\u0000class that naturally generalizes planarity and linklessness. We verify several\u0000conjectures of van der Holst; in particular, we prove that each of the 78\u0000graphs of the Heawood family is an excluded minor for the class of 4-flat\u0000graphs.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"52 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192257","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}
引用次数: 0
Virtual Braids and Cluster Algebras 虚拟辫和簇代数
arXiv - MATH - Geometric Topology Pub Date : 2024-08-22 DOI: arxiv-2408.12684
Andrey Egorov
{"title":"Virtual Braids and Cluster Algebras","authors":"Andrey Egorov","doi":"arxiv-2408.12684","DOIUrl":"https://doi.org/arxiv-2408.12684","url":null,"abstract":"In 2015 Hikami and Inoue constructed a representation of the braid group in\u0000terms of cluster algebra associated with the decomposition of the complement of\u0000the corresponding knot into ideal hyperbolic tetrahedra. This representation\u0000leads to the calculation of the hyperbolic volume of the complement of the knot\u0000that is the closure of the corresponding braid. In this paper, based on the\u0000Hikami-Inoue representation discussed above, we construct a representation for\u0000the virtual braid group. We show that the so-called \"forbidden relations\" do\u0000not hold in the image of the resulting representation. In addition, based on\u0000the developed method, we construct representations for the flat braid group and\u0000the flat virtual braid group.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"80 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192255","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}
引用次数: 0
Multivariate Alexander quandles, VI. Metabelian groups and 2-component links 多元亚历山大广数，VI.元胞群和 2 分量联系
arXiv - MATH - Geometric Topology Pub Date : 2024-08-21 DOI: arxiv-2408.11784
Lorenzo Traldi
{"title":"Multivariate Alexander quandles, VI. Metabelian groups and 2-component links","authors":"Lorenzo Traldi","doi":"arxiv-2408.11784","DOIUrl":"https://doi.org/arxiv-2408.11784","url":null,"abstract":"We prove two properties of the modules and quandles discussed in this series.\u0000First, the fundamental multivariate Alexander quandle $Q_A(L)$ is isomorphic to\u0000the natural image of the fundamental quandle in the metabelian quotient\u0000$G(L)/G(L)''$ of the link group. Second, the medial quandle of a classical\u00002-component link $L$ is determined by the reduced Alexander invariant of $L$.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"75 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192259","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}
引用次数: 0
A topological proof of Wolpert's formula for the Weil-Petersson symplectic form in terms of the Fenchel-Nielsen coordinates 用芬切尔-尼尔森坐标证明魏尔-彼得森对称形式的沃尔佩特公式的拓扑证明
arXiv - MATH - Geometric Topology Pub Date : 2024-08-09 DOI: arxiv-2408.04937
Nariya Kawazumi
{"title":"A topological proof of Wolpert's formula for the Weil-Petersson symplectic form in terms of the Fenchel-Nielsen coordinates","authors":"Nariya Kawazumi","doi":"arxiv-2408.04937","DOIUrl":"https://doi.org/arxiv-2408.04937","url":null,"abstract":"We introduce a natural cell decomposition of a closed oriented surface\u0000associated with a pants decomposition, and an explicit groupoid cocycle on the\u0000cell decomposition which represents each point of the Teichm\"uller space\u0000$mathcal{T}_g$. We call it the {it standard cocycle} of the point of\u0000$mathcal{T}_g$. As an application of the explicit description of the standard\u0000cocycle, we obtain a topological proof of Wolpert's formula for the\u0000Weil-Petersson symplectic form in terms of the Fenchel-Nielsen coordinates\u0000associated with the pants decomposition.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"103 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141942483","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}
引用次数: 0
Cusp-transitive 4-manifolds with every cusp section 具有每个尖顶截面的尖顶-横截4-网格
arXiv - MATH - Geometric Topology Pub Date : 2024-08-09 DOI: arxiv-2408.05080
Jacopo Guoyi Chen, Edoardo Rizzi
{"title":"Cusp-transitive 4-manifolds with every cusp section","authors":"Jacopo Guoyi Chen, Edoardo Rizzi","doi":"arxiv-2408.05080","DOIUrl":"https://doi.org/arxiv-2408.05080","url":null,"abstract":"We realize every closed flat 3-manifold as a cusp section of a complete,\u0000finite-volume hyperbolic 4-manifold whose symmetry group acts transitively on\u0000the set of cusps. Moreover, for every such 3-manifold, a dense subset of its\u0000flat metrics can be realized as cusp sections of a cusp-transitive 4-manifold.\u0000Finally, we prove that there are a lot of 4-manifolds with pairwise isometric\u0000cusps, for any given cusp type.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141942482","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}
引用次数: 0
On compact complex surfaces with finite homotopy rank-sum 关于具有有限同调秩和的紧凑复曲面
arXiv - MATH - Geometric Topology Pub Date : 2024-08-08 DOI: arxiv-2408.04558
Indranil Biswas, Buddhadev Hajra
{"title":"On compact complex surfaces with finite homotopy rank-sum","authors":"Indranil Biswas, Buddhadev Hajra","doi":"arxiv-2408.04558","DOIUrl":"https://doi.org/arxiv-2408.04558","url":null,"abstract":"A topological space (not necessarily simply connected) is said to have finite\u0000homotopy rank-sum if the sum of the ranks of all higher homotopy groups (from\u0000the second homotopy group onward) is finite. In this article, we characterize\u0000the smooth compact complex Kaehler surfaces having finite homotopy rank-sum. We\u0000also prove the Steinness of the universal cover of these surfaces assuming\u0000holomorphic convexity of the universal cover.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"103 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141942489","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}
引用次数: 0
Classifying the surface-knot modules 面结模块的分类
arXiv - MATH - Geometric Topology Pub Date : 2024-08-08 DOI: arxiv-2408.04285
Akio Kawauchi
{"title":"Classifying the surface-knot modules","authors":"Akio Kawauchi","doi":"arxiv-2408.04285","DOIUrl":"https://doi.org/arxiv-2408.04285","url":null,"abstract":"The $k$th module of a surface-knot of a genus $g$ in the 4-sphere is the $k$th integral homology module of the infinite cyclic covering of the\u0000surface-knot complement. The reduced first module is the quotient module of the first\u0000module by the finite sub-module defining the torsion linking. It is shown that the reduced first\u0000module for every genus $g$ is characterized in terms of properties of a finitely generated\u0000module. As a by-product, a concrete example of the fundamental group of a surface-knot of\u0000genus $g$ which is not the fundamental group of any surface-knot of genus $g-1$ is\u0000given for every $g>0$. The torsion part and the torsion-free part of the second module are\u0000determined by the reduced first module and the genus-class on the reduced first module. The\u0000third module vanishes. The concept of an exact leaf of a surface-knot is introduced, whose\u0000linking is an orthogonal sum of the torsion linking and a hyperbolic linking.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141942487","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}
引用次数: 0
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：604180095
Book学术官方微信