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Another proof of free ribbon lemma 自由缎带定理的另一个证明
arXiv - MATH - Geometric Topology Pub Date : 2024-08-08 DOI: arxiv-2408.04793
Akio Kawauchi
{"title":"Another proof of free ribbon lemma","authors":"Akio Kawauchi","doi":"arxiv-2408.04793","DOIUrl":"https://doi.org/arxiv-2408.04793","url":null,"abstract":"Free ribbon lemma that every free sphere-link in the 4-sphere is a ribbon\u0000sphere-link is shown in an earlier paper by the author. In this paper, another\u0000proof of this lemma is given.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"104 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141942484","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
Electric group for knots and links 结和链接的电组
arXiv - MATH - Geometric Topology Pub Date : 2024-08-08 DOI: arxiv-2408.04510
Philipp Korablev
{"title":"Electric group for knots and links","authors":"Philipp Korablev","doi":"arxiv-2408.04510","DOIUrl":"https://doi.org/arxiv-2408.04510","url":null,"abstract":"In 2014 Andrey Perfiliev introduced the so-called electric invariant for\u0000non-oriented knots. This invariant was motivated by using Kirchhoff's laws for\u0000the dual graph of the knot diagram. Later, in 2020, Anastasiya Galkina\u0000generalised this invariant and defined the electric group for non-oriented\u0000knots. Both works were never written and published. In the present paper we\u0000describe a simple and general approach to the electric group for oriented knots\u0000and links. Each homomorphism from the electric group to an arbitrary finite\u0000group can be described by a proper colouring of the diagram. This colouring\u0000assigns an element of the group to each crossing of the diagram, and the proper\u0000conditions correspond to the areas of the diagram. In the second part of the\u0000paper we introduce tensor network invariants for coloured links. The idea of\u0000these invariants is very close to quantum invariants for classical links.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141942486","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
Geometric representations of the braid group on a nonorientable surface 非定向面上辫状群的几何表示
arXiv - MATH - Geometric Topology Pub Date : 2024-08-08 DOI: arxiv-2408.04707
Michał Stukow, Błażej Szepietowski
{"title":"Geometric representations of the braid group on a nonorientable surface","authors":"Michał Stukow, Błażej Szepietowski","doi":"arxiv-2408.04707","DOIUrl":"https://doi.org/arxiv-2408.04707","url":null,"abstract":"We classify homomorphisms from the braid group on $n$ strands to the pure\u0000mapping class group of a nonoriantable surface of genus $g$. For $nge 14$ and\u0000$gle 2lfloor{n/2}rfloor+1$ every such homomorphism is either cyclic, or it\u0000maps standard generators of the braid group to either distinct Dehn twists, or\u0000distinct crosscap transpositions, possibly multiplied by the same element of\u0000the centralizer of the image.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"263 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141942485","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
Fibered ribbon pretzels 纤维丝带椒盐脆饼
arXiv - MATH - Geometric Topology Pub Date : 2024-08-07 DOI: arxiv-2408.03644
Ana G. Lecuona, Andy Wand
{"title":"Fibered ribbon pretzels","authors":"Ana G. Lecuona, Andy Wand","doi":"arxiv-2408.03644","DOIUrl":"https://doi.org/arxiv-2408.03644","url":null,"abstract":"We classify fibered ribbon pretzel knots up to mutation. The classification\u0000is complete, except perhaps for members of Lecuona's ``exceptional'' family of\u0000[Lec15]. The result is obtained by combining lattice embedding techniques with\u0000Gabai's classification of fibered pretzel knots, and exhibiting ribbon disks,\u0000some of which lie outside of known patterns for standard pretzel projections.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141942490","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 pattern for torsion in Khovanov homology 霍瓦诺夫同构中的扭转模式
arXiv - MATH - Geometric Topology Pub Date : 2024-08-07 DOI: arxiv-2408.03721
R. Díaz, P. M. G. Manchón
{"title":"A pattern for torsion in Khovanov homology","authors":"R. Díaz, P. M. G. Manchón","doi":"arxiv-2408.03721","DOIUrl":"https://doi.org/arxiv-2408.03721","url":null,"abstract":"We prove that certain specific sum of enhanced states produce torsion of\u0000order two in the Khovanov homology.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141942488","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
Finiteness of totally geodesic hypersurfaces 完全大地超曲面的有限性
arXiv - MATH - Geometric Topology Pub Date : 2024-08-06 DOI: arxiv-2408.03430
Simion Filip, David Fisher, Ben Lowe
{"title":"Finiteness of totally geodesic hypersurfaces","authors":"Simion Filip, David Fisher, Ben Lowe","doi":"arxiv-2408.03430","DOIUrl":"https://doi.org/arxiv-2408.03430","url":null,"abstract":"We prove that a negatively curved analytic Riemannian manifold that contains\u0000infinitely many totally geodesic hypersurfaces is isometric to an arithmetic\u0000hyperbolic manifold.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"79 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141942492","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
Splitting of homotopy idempotents revisited 再论同调幂等式的分裂
arXiv - MATH - Geometric Topology Pub Date : 2024-08-05 DOI: arxiv-2408.02785
Jerzy Dydak
{"title":"Splitting of homotopy idempotents revisited","authors":"Jerzy Dydak","doi":"arxiv-2408.02785","DOIUrl":"https://doi.org/arxiv-2408.02785","url":null,"abstract":"We are presenting proofs of fundamental results related to homotopy\u0000idempotents, proofs that are sufficiently simple so that even the author can\u0000understand them. The first one is that homotopy idempotents in the category of\u0000pointed connected CW complexes split and the second one is that unpointed\u0000homotopy idempotents in the category of finite-dimensional CW complexes split.\u0000Some of our proofs rectify gaps in the existing literature.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141942493","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
Correction terms of double branched covers and symmetries of immersed curves 双支盖的修正项和沉浸曲线的对称性
arXiv - MATH - Geometric Topology Pub Date : 2024-08-05 DOI: arxiv-2408.02857
Jonathan Hanselman, Marco Marengon, Biji Wong
{"title":"Correction terms of double branched covers and symmetries of immersed curves","authors":"Jonathan Hanselman, Marco Marengon, Biji Wong","doi":"arxiv-2408.02857","DOIUrl":"https://doi.org/arxiv-2408.02857","url":null,"abstract":"We use the immersed curves description of bordered Floer homology to study\u0000$d$-invariants of double branched covers $Sigma_2(L)$ of arborescent links $L\u0000subset S^3$. We define a new invariant $Delta_{sym}$ of bordered\u0000$mathbb{Z}_2$-homology solid tori from an involution of the associated\u0000immersed curves and relate it to both the $d$-invariants and the\u0000Neumann-Siebenmann $barmu$-invariants of certain fillings. We deduce that if\u0000$L$ is a 2-component arborescent link and $Sigma_2(L)$ is an L-space, then the\u0000spin $d$-invariants of $Sigma_2(L)$ are determined by the signatures of $L$.\u0000By a separate argument, we show that the same relationship holds when $L$ is a\u00002-component link that admits a certain symmetry.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"59 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141942491","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
The symmetric slice of ${rm SL}(3,mathbb{C})$-character variety of the Whitehead link 白石链接的${rm SL}(3,mathbb{C})$特征变量的对称切片
arXiv - MATH - Geometric Topology Pub Date : 2024-08-05 DOI: arxiv-2408.02334
Haimiao Chen
{"title":"The symmetric slice of ${rm SL}(3,mathbb{C})$-character variety of the Whitehead link","authors":"Haimiao Chen","doi":"arxiv-2408.02334","DOIUrl":"https://doi.org/arxiv-2408.02334","url":null,"abstract":"We give a nice description for a Zariski open subset of the ${rm\u0000SL}(3,mathbb{C})$-character variety of the Whitehead link.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141942494","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
Topology of hyperplane arrangements via real structure 通过实结构的超平面排列拓扑
arXiv - MATH - Geometric Topology Pub Date : 2024-08-04 DOI: arxiv-2408.02038
Masahiko Yoshinaga
{"title":"Topology of hyperplane arrangements via real structure","authors":"Masahiko Yoshinaga","doi":"arxiv-2408.02038","DOIUrl":"https://doi.org/arxiv-2408.02038","url":null,"abstract":"This note is a survey on the topology of hyperplane arrangements. We mainly\u0000focus on the relationship between topology and the real structure, such as\u0000adjacent relations of chambers and stratifications related to real structures.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"2012 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141942495","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
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