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A Geometric Compactification Of The Moduli Stack Of Left Invariant Complex Structures On A Lie Group 李群上左不变复结构模数堆的几何紧凑性
arXiv - MATH - Geometric Topology Pub Date : 2024-08-29 DOI: arxiv-2408.16182
Laurent Meersseman
{"title":"A Geometric Compactification Of The Moduli Stack Of Left Invariant Complex Structures On A Lie Group","authors":"Laurent Meersseman","doi":"arxiv-2408.16182","DOIUrl":"https://doi.org/arxiv-2408.16182","url":null,"abstract":"We describe a geometric compactification of the moduli stack of left\u0000invariant complex structures on a fixed real Lie group or a fixed quotient. The\u0000extra points are CR structures transverse to a real foliation.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192081","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 note on the pure cactus group of degree three and the configuration space of four points on the circle 关于三度纯仙人掌群和圆上四点构型空间的说明
arXiv - MATH - Geometric Topology Pub Date : 2024-08-28 DOI: arxiv-2408.15478
Takatoshi Hama, Kazuhiro Ichihara
{"title":"A note on the pure cactus group of degree three and the configuration space of four points on the circle","authors":"Takatoshi Hama, Kazuhiro Ichihara","doi":"arxiv-2408.15478","DOIUrl":"https://doi.org/arxiv-2408.15478","url":null,"abstract":"The cactus group was introduced by Henriques and Kamnitzer as an analogue of\u0000the braid group. In this note, we provide an explicit description of the\u0000relationship between the pure cactus group of degree three and the\u0000configuration space of four points on the circle.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192079","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 Benard-Conway invariant of two-component links 双成分链接的贝纳德-康威不变量
arXiv - MATH - Geometric Topology Pub Date : 2024-08-28 DOI: arxiv-2408.16161
Zedan Liu, Nikolai Saveliev
{"title":"The Benard-Conway invariant of two-component links","authors":"Zedan Liu, Nikolai Saveliev","doi":"arxiv-2408.16161","DOIUrl":"https://doi.org/arxiv-2408.16161","url":null,"abstract":"The Benard-Conway invariant of links in the 3-sphere is a Casson-Lin type\u0000invariant defined by counting irreducible SU(2) representations of the link\u0000group with fixed meridional traces. For two-component links with linking number\u0000one, the invariant has been shown to equal a symmetrized multivariable link\u0000signature. We extend this result to all two-component links with non-zero\u0000linking number. A key ingredient in the proof is an explicit calculation of the\u0000Benard-Conway invariant for (2, 2l)-torus links with the help of the Chebyshev\u0000polynomials.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192082","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
Computing Finite Type Invariants Efficiently 高效计算有限类型不变式
arXiv - MATH - Geometric Topology Pub Date : 2024-08-28 DOI: arxiv-2408.15942
Dror Bar-Natan, Itai Bar-Natan, Iva Halacheva, Nancy Scherich
{"title":"Computing Finite Type Invariants Efficiently","authors":"Dror Bar-Natan, Itai Bar-Natan, Iva Halacheva, Nancy Scherich","doi":"arxiv-2408.15942","DOIUrl":"https://doi.org/arxiv-2408.15942","url":null,"abstract":"We describe an efficient algorithm to compute finite type invariants of type\u0000$k$ by first creating, for a given knot $K$ with $n$ crossings, a look-up table\u0000for all subdiagrams of $K$ of size $lceil frac{k}{2}rceil$ indexed by dyadic\u0000intervals in $[0,2n-1]$. Using this algorithm, any such finite type invariant\u0000can be computed on an $n$-crossing knot in time $sim n^{lceil\u0000frac{k}{2}rceil}$, a lot faster than the previously best published bound of\u0000$sim n^k$.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"75 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192246","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
Homogeneous braids are visually prime 同质辫在视觉上是质数
arXiv - MATH - Geometric Topology Pub Date : 2024-08-28 DOI: arxiv-2408.15730
Peter Feller, Lukas Lewark, Miguel Orbegozo Rodriguez
{"title":"Homogeneous braids are visually prime","authors":"Peter Feller, Lukas Lewark, Miguel Orbegozo Rodriguez","doi":"arxiv-2408.15730","DOIUrl":"https://doi.org/arxiv-2408.15730","url":null,"abstract":"We show that closures of homogeneous braids are visually prime, addressing a\u0000question of Cromwell. The key technical tool for the proof is the following\u0000criterion concerning primeness of open books, which we consider to be of\u0000independent interest. For open books of 3-manifolds the property of having no\u0000fixed essential arcs is preserved under essential Murasugi sums with a strictly\u0000right-veering open book, if the plumbing region of the original open book veers\u0000to the left. We also provide examples of open books in S^3 demonstrating that\u0000primeness is not necessarily preserved under essential Murasugi sum, in fact\u0000not even under stabilizations a.k.a. Hopf plumbings. Furthermore, we find that\u0000trefoil plumbings need not preserve primeness. In contrast, we establish that\u0000figure-eight knot plumbings do preserve primeness.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"42 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142224775","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 note on the unknotting number and the region unknotting number of weaving knots 关于织结的解结数和区域解结数的说明
arXiv - MATH - Geometric Topology Pub Date : 2024-08-27 DOI: arxiv-2408.14938
Ayaka Shimizu, Amrendra Gill, Sahil Joshi
{"title":"A note on the unknotting number and the region unknotting number of weaving knots","authors":"Ayaka Shimizu, Amrendra Gill, Sahil Joshi","doi":"arxiv-2408.14938","DOIUrl":"https://doi.org/arxiv-2408.14938","url":null,"abstract":"A weaving knot is an alternating knot whose minimal diagram is a closed braid\u0000of a lattice-like pattern. In this paper, upper bounds of the unknotting number\u0000and the region unknotting number for some families of weaving knots are given\u0000by diagrammatical and combinatorial examination of the warping degree of\u0000weaving knot diagrams.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"132 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192248","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
Angle structure on general hyperbolic 3-manifolds 一般双曲3-manifolds上的角度结构
arXiv - MATH - Geometric Topology Pub Date : 2024-08-26 DOI: arxiv-2408.14003
Ge Huabin, Jia Longsong, Zhang Faze
{"title":"Angle structure on general hyperbolic 3-manifolds","authors":"Ge Huabin, Jia Longsong, Zhang Faze","doi":"arxiv-2408.14003","DOIUrl":"https://doi.org/arxiv-2408.14003","url":null,"abstract":"Let $M$ be a non-compact hyperbolic $3$-manifold with finite volume and\u0000totally geodesic boundary components. By subdividing mixed ideal polyhedral\u0000decompositions of $M$, under some certain topological conditions, we prove that\u0000$M$ has an ideal triangulation which admits an angle structure.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192249","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
Localization and the Floer homology of strongly invertible knots 强反转结的局部性和弗洛尔同源性
arXiv - MATH - Geometric Topology Pub Date : 2024-08-25 DOI: arxiv-2408.13892
Aakash Parikh
{"title":"Localization and the Floer homology of strongly invertible knots","authors":"Aakash Parikh","doi":"arxiv-2408.13892","DOIUrl":"https://doi.org/arxiv-2408.13892","url":null,"abstract":"We establish two spectral sequences in knot Floer homology associated to a\u0000directed strongly invertible knot K: one from the knot Floer homology of K to a\u0000two dimensional vector space, and one from the singular knot Floer homology of\u0000a singular knot associated to K to the knot Floer homology quotient knot of K.\u0000The first of these spectral sequences is used to define a numerical invariant\u0000of strongly invertible knots.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192253","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
Embedding periodic maps of surfaces into those of spheres with minimal dimensions 以最小维度将曲面的周期映射嵌入到球面的周期映射中
arXiv - MATH - Geometric Topology Pub Date : 2024-08-25 DOI: arxiv-2408.13749
Chao Wang, Shicheng Wang, Zhongzi Wang
{"title":"Embedding periodic maps of surfaces into those of spheres with minimal dimensions","authors":"Chao Wang, Shicheng Wang, Zhongzi Wang","doi":"arxiv-2408.13749","DOIUrl":"https://doi.org/arxiv-2408.13749","url":null,"abstract":"It is known that any periodic map of order $n$ on a closed oriented surface\u0000of genus $g$ can be equivariantly embedded into $S^m$ for some $m$. In the\u0000orientable and smooth category, we determine the smallest possible $m$ when\u0000$ngeq 3g$. We show that for each integer $k>1$ there exist infinitely many\u0000periodic maps such that the smallest possible $m$ is equal to $k$.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192251","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
Relative train tracks and endperiodic graph maps 相对列车轨道和端周期图谱
arXiv - MATH - Geometric Topology Pub Date : 2024-08-23 DOI: arxiv-2408.13401
Yan Mary He, Chenxi Wu
{"title":"Relative train tracks and endperiodic graph maps","authors":"Yan Mary He, Chenxi Wu","doi":"arxiv-2408.13401","DOIUrl":"https://doi.org/arxiv-2408.13401","url":null,"abstract":"We study endperiodic maps of an infinite graph with finitely many ends. We\u0000prove that any such map is homotopic to an endperiodic relative train track\u0000map. Moreover, we show that the (largest) Perron-Frobenius eigenvalue of the\u0000transition matrix is a canonical quantity associated to the map.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192252","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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