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Strongly irreducible Heegaard splittings of hyperbolic 3-manifolds 双曲型3-流形的强不可约性
arXiv: Geometric Topology Pub Date : 2019-11-27 DOI: 10.1090/proc/15114
Tejas Kalelkar
{"title":"Strongly irreducible Heegaard splittings of hyperbolic 3-manifolds","authors":"Tejas Kalelkar","doi":"10.1090/proc/15114","DOIUrl":"https://doi.org/10.1090/proc/15114","url":null,"abstract":"Colding and Gabai have given an effective version of Li's theorem that non-Haken hyperbolic 3-manifolds have finitely many irreducible Heegaard splittings. As a corollary of their work, we show that Haken hyperbolic 3-manifolds have a finite collection of strongly irreducible Heegaard surfaces $S_i$ and incompressible surfaces $K_j$ such that any strongly irreducible Heegaard surface is a Haken sum $S_i + sum_j n_j K_j$, up to one-sided associates of the Heegaard surfaces.","PeriodicalId":8454,"journal":{"name":"arXiv: Geometric Topology","volume":"60 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77243736","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
Contact structures, excisions and sutured monopole Floer homology 接触结构、切除与缝合单极花同源性
arXiv: Geometric Topology Pub Date : 2019-11-25 DOI: 10.2140/agt.2020.20.2553
Zhenkun Li
{"title":"Contact structures, excisions and sutured monopole Floer homology","authors":"Zhenkun Li","doi":"10.2140/agt.2020.20.2553","DOIUrl":"https://doi.org/10.2140/agt.2020.20.2553","url":null,"abstract":"In this paper, we explore the interplay between contact structures and sutured monopole Floer homology. First, we study the behavior of contact elements, which were defined by Baldwin and Sivek, under the operation of performing Floer excisions, which was introduced to the context of sutured monopole Floer homology by Kronheimer and Mrowka. We then compute the sutured monopole Floer homology of some special balanced sutured manifolds, using tools closely related to contact geometry. For application, we obtain an exact triangle for the oriented skein relation in monopole theory and derive a connected sum formula for sutured monopole Floer homology.","PeriodicalId":8454,"journal":{"name":"arXiv: Geometric Topology","volume":"69 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86142885","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: 9
On 3-dimensional homotopy quantum field theory III: Comparison of two approaches 三维同伦量子场论III:两种方法的比较
arXiv: Geometric Topology Pub Date : 2019-11-22 DOI: 10.1142/s0129167x20500767
V. Turaev, A. Virelizier
{"title":"On 3-dimensional homotopy quantum field theory III: Comparison of two approaches","authors":"V. Turaev, A. Virelizier","doi":"10.1142/s0129167x20500767","DOIUrl":"https://doi.org/10.1142/s0129167x20500767","url":null,"abstract":"Let G be a discrete group and C be an additive spherical G-fusion category. We prove that the state sum 3-dimensional HQFT derived from C is isomorphic to the surgery 3-dimensional HQFT derived from the G-center of C.","PeriodicalId":8454,"journal":{"name":"arXiv: Geometric Topology","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82233992","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: 8
Local Limits of Connected Subgroups of SL 3 (ℝ) SL 3 (l)连通子群的局部极限
arXiv: Geometric Topology Pub Date : 2019-11-21 DOI: 10.5802/CRMATH.160
Nir Lazarovich, Arielle Leitner
{"title":"Local Limits of Connected Subgroups of SL 3 (ℝ)","authors":"Nir Lazarovich, Arielle Leitner","doi":"10.5802/CRMATH.160","DOIUrl":"https://doi.org/10.5802/CRMATH.160","url":null,"abstract":"We compute all local limits of all connected subgroups of $SL_3(mathbb{R})$ in the Chabauty topology","PeriodicalId":8454,"journal":{"name":"arXiv: Geometric Topology","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76230363","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: 3
Thin subgroups isomorphic toGromov–Piatetski-Shapiro lattices gromov - piatetski - shapiro格同构的细亚群
arXiv: Geometric Topology Pub Date : 2019-11-16 DOI: 10.2140/PJM.2020.309.257
Samuel A. Ballas
{"title":"Thin subgroups isomorphic to\u0000Gromov–Piatetski-Shapiro lattices","authors":"Samuel A. Ballas","doi":"10.2140/PJM.2020.309.257","DOIUrl":"https://doi.org/10.2140/PJM.2020.309.257","url":null,"abstract":"In this paper we produce many examples of thin subgroups of special linear groups that are isomorphic to the fundamental groups of non-arithmetic hyperbolic manifolds. Specifically, we show that the non-arithmetic lattices in $mathrm{SO}(n,1)$ constructed by Gromov and Piateski-Shapiro can be embedded into $mathrm{SL}_{n+1}(mathbb{R})$ so that their images are thin subgroups","PeriodicalId":8454,"journal":{"name":"arXiv: Geometric Topology","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76142137","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
Fibrations of $mathbb{R}^3$ by oriented lines $mathbb{R}^3$的定向线的纤维
arXiv: Geometric Topology Pub Date : 2019-11-15 DOI: 10.2140/agt.2021.21.2899
Michael C. Harrison
{"title":"Fibrations of $mathbb{R}^3$ by oriented lines","authors":"Michael C. Harrison","doi":"10.2140/agt.2021.21.2899","DOIUrl":"https://doi.org/10.2140/agt.2021.21.2899","url":null,"abstract":"A fibration of $mathbb{R}^3$ by oriented lines is given by a unit vector field $V : mathbb{R}^3 to S^2$, for which all of the integral curves are oriented lines. A line fibration is called skew if no two fibers are parallel. Skew fibrations have been the focus of recent study, in part due to their close relationships with great circle fibrations of $S^3$ and with tight contact structures on $mathbb{R}^3$. Both geometric and topological classifications of the space of skew fibrations have appeared; these classifications rely on certain rigid geometric properties exhibited by skew fibrations. Here we study these properties for line fibrations which are not necessarily skew, and we offer some partial answers to the question: in what sense do nonskew fibrations look and behave like skew fibrations? We develop and utilize a technique, called the parallel plane pushoff, for studying nonskew fibrations. In addition, we summarize the known relationship between line fibrations and contact structures, and we extend these results to give a complete correspondence. Finally, we develop a technique for generating nonskew fibrations and offer a number of examples.","PeriodicalId":8454,"journal":{"name":"arXiv: Geometric Topology","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90522409","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: 3
On the discreteness of states accessible via right-angled paths in hyperbolic space 双曲空间直角路径可达状态的离散性
arXiv: Geometric Topology Pub Date : 2019-11-15 DOI: 10.4171/LEM/66-3/4-4
E. García, Pablo Lessa
{"title":"On the discreteness of states accessible via right-angled paths in hyperbolic space","authors":"E. García, Pablo Lessa","doi":"10.4171/LEM/66-3/4-4","DOIUrl":"https://doi.org/10.4171/LEM/66-3/4-4","url":null,"abstract":"We consider the control problem where, given an orthonormal tangent frame in the hyperbolic plane or three dimensional hyperbolic space, one is allowed to transport the frame a fixed distance $r > 0$ along the geodesic in direction of the first vector, or rotate it in place a right angle. We characterize the values of $r > 0$ for which the set of orthonormal frames accessible using these transformations is discrete. \u0000In the hyperbolic plane this is equivalent to solving the discreteness problem for a particular one parameter family of two-generator subgroups of $PSL_2(mathbb{R})$. In the three dimensional case we solve this problem for a particular one parameter family of subgroups of the isometry group which have four generators.","PeriodicalId":8454,"journal":{"name":"arXiv: Geometric Topology","volume":"99 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85820041","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
Finite, fiber-preserving group actions on elliptic 3-manifolds 椭圆型3流形上有限的保纤维群作用
arXiv: Geometric Topology Pub Date : 2019-11-08 DOI: 10.5666/KMJ.2022.62.2.363
Benjamin Peet
{"title":"Finite, fiber-preserving group actions on elliptic 3-manifolds","authors":"Benjamin Peet","doi":"10.5666/KMJ.2022.62.2.363","DOIUrl":"https://doi.org/10.5666/KMJ.2022.62.2.363","url":null,"abstract":"In two previous papers the author presented a general construction of finite, fiber- and orientation-preserving group actions on orientable Seifert manifolds. In this paper we restrict our attention to elliptic 3-manifolds. A proof is given that orientation-reversing and fiber-preserving diffeomorphisms of Seifert manifolds do not exist for nonzero Euler class, in particular elliptic 3-manifolds. Each type of elliptic 3-manifold is then considered and the possible group actions that fit the given construction. This is shown to be all but a few cases that have been considered elsewhere. Finally, a presentation for the quotient space under such an action is constructed and a specific example is generated.","PeriodicalId":8454,"journal":{"name":"arXiv: Geometric Topology","volume":"67 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72802377","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
Region crossing change on spatial theta-curves 空间theta曲线上的区域交叉变化
arXiv: Geometric Topology Pub Date : 2019-10-27 DOI: 10.1142/s0218216520500285
Ayaka Shimizu, R. Takahashi
{"title":"Region crossing change on spatial theta-curves","authors":"Ayaka Shimizu, R. Takahashi","doi":"10.1142/s0218216520500285","DOIUrl":"https://doi.org/10.1142/s0218216520500285","url":null,"abstract":"A region crossing change at a region of a spatial-graph diagram is a transformation changing every crossing on the boundary of the region. In this paper, it is shown that every spatial graph consisting of theta-curves can be unknotted by region crossing changes.","PeriodicalId":8454,"journal":{"name":"arXiv: Geometric Topology","volume":"42 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82076196","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: 2
The diameter of random Belyi surfaces 随机贝伊曲面的直径
arXiv: Geometric Topology Pub Date : 2019-10-25 DOI: 10.2140/agt.2021.21.2929
Thomas Budzinski, N. Curien, Bram Petri
{"title":"The diameter of random Belyi surfaces","authors":"Thomas Budzinski, N. Curien, Bram Petri","doi":"10.2140/agt.2021.21.2929","DOIUrl":"https://doi.org/10.2140/agt.2021.21.2929","url":null,"abstract":"We determine the asymptotic growth rate of the diameter of the random hyperbolic surfaces constructed by Brooks and Makover. This model consists of a uniform gluing of $2n$ hyperbolic ideal triangles along their sides followed by a compactification to get a random hyperbolic surface of genus roughly $n/2$. We show that the diameter of those random surfaces is asymptotic to $2 log n$ in probability as $n to infty$.","PeriodicalId":8454,"journal":{"name":"arXiv: Geometric Topology","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89691285","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: 8
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