Geometric Topology

Authors and titles for August 2025

[1] arXiv:2508.00184 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Schoenflies problem for area preserving biLipschitz mappings Show Chinese title

Title: Schoenflies问题对于保面积双Lipschitz映射

Maxim Prasolov

Subjects: Geometric Topology (math.GT) ; Functional Analysis (math.FA)

[2] arXiv:2508.00297 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Peripheral subgroups of Kleinian groups Show Chinese title

Title: 克莱因群的外围子群

Alex Elzenaar

Comments: 36 pages, 9 figures

Subjects: Geometric Topology (math.GT) ; Complex Variables (math.CV) ; Group Theory (math.GR)

[3] arXiv:2508.00606 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: New torsion patterns in Khovanov homology Show Chinese title

Title: Khovanov同调中的新扭结模式

Raquel Díaz, Pedro M. G. Manchón

Comments: 25 pages, 21 figures

Subjects: Geometric Topology (math.GT)

[4] arXiv:2508.00644 (cross-list from math.GT) [cn-pdf, pdf, other]

Title: 2-cabling and tangle operators in Khovanov theory Show Chinese title

Title: 2交叉和辫子算子在科霍诺夫理论中

Mihai Marian

Comments: 45 pages, many figures, comments welcome

Subjects: Geometric Topology (math.GT)

[5] arXiv:2508.01185 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Homotopy Type of the Space of Fibrations of the Three-sphere by Simple Closed Curves Show Chinese title

Title: 三维球面沿简单闭曲线的纤维空间的同伦类型

Dennis Deturck, Ziqi Fang, Herman Gluck, Leandro Lichtenfelz, Mona Merling, Yi Wang, Jingye Yang

Comments: 35 pages, 13 figures

Subjects: Geometric Topology (math.GT) ; Algebraic Topology (math.AT) ; Differential Geometry (math.DG)

[6] arXiv:2508.01629 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Topology of boundary special generic maps into Euclidean spaces Show Chinese title

Title: 边界特殊泛函映射到欧几里得空间的拓扑结构

Koki Iwakura

Comments: 8 pages, 1 figure

Subjects: Geometric Topology (math.GT)

[7] arXiv:2508.02017 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Exotic $\mathbb{R}^4$'s with Compactly Supported Diffeomorphisms Show Chinese title

Title: 奇异$\mathbb{R}^4$的紧支微分同胚

Abhishek Shivkumar

Subjects: Geometric Topology (math.GT)

[8] arXiv:2508.02535 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Kauffman bracket polynomials, perfect matchings and cluster variables Show Chinese title

Title: Kauffman括号多项式，完美匹配和簇变量

Weiqing Tian

Comments: 37 pages, 20 figures

Subjects: Geometric Topology (math.GT) ; General Topology (math.GN)

[9] arXiv:2508.02897 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Fibrations on Handlebodies Show Chinese title

Title: 流形上的纤维化

Jesús Hernández Hernández, Christopher J. Leininger, Ferrán Valdez

Comments: 22 pages, 11 Figures

Subjects: Geometric Topology (math.GT)

[10] arXiv:2508.03013 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Pointed Racks and Their Applications to Braid Theory Show Chinese title

Title: 指向的rack及其在辫子理论中的应用

Angel Apollos, Jose Ceniceros

Subjects: Geometric Topology (math.GT)

[11] arXiv:2508.03260 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Existence and deformability of topological Morse functions Show Chinese title

Title: 拓扑莫尔斯函数的存在性和可变形性

Ingrid Irmer

Subjects: Geometric Topology (math.GT)

[12] arXiv:2508.03353 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Linear Bound for Kakimizu Complex Diameter of Hyperbolic Knots Show Chinese title

Title: 双曲纽结的Kakimizu复形直径的线性界

Xiao Chen, Wujie Shen

Comments: 15 pages, 10 figures. Comments are welcome!

Subjects: Geometric Topology (math.GT)

[13] arXiv:2508.03394 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Instanton 2-torsion and Dehn surgeries Show Chinese title

Title: 瞬子2阶挠和德恩手术

Zhenkun Li, Fan Ye

Comments: 30 pages, 5 figures. Comments are welcome

Subjects: Geometric Topology (math.GT)

[14] arXiv:2508.03897 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: A note on real Heegaard Floer homology and localization Show Chinese title

Title: 关于实Heegaard Floer同调和局部化的一篇注记

Kristen Hendricks

Comments: 24 pages, 1 figure. Comments welcome!

Subjects: Geometric Topology (math.GT) ; Symplectic Geometry (math.SG)

[15] arXiv:2508.04042 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Loops of handleslides for sutured diagrams Show Chinese title

Title: 带有手柄滑动的缝合图的环

Qianhe Qin

Comments: 26 pages, 20 figures

Subjects: Geometric Topology (math.GT)

[16] arXiv:2508.04587 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Schmutz-Thurston Duality Show Chinese title

Title: 施穆茨-塔尔斯顿对偶

Ingrid Irmer

Subjects: Geometric Topology (math.GT)

[17] arXiv:2508.04813 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Topology of the space of $d$-pleated surfaces Show Chinese title

Title: $d$-折曲面空间的拓扑结构

Sara Maloni, Giuseppe Martone, Filippo Mazzoli, Tengren Zhang

Comments: 69 pages, 17 figures. Comments are welcome!

Subjects: Geometric Topology (math.GT)

[18] arXiv:2508.05000 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Topological components of surface group representations and signature Show Chinese title

Title: 曲面群表示的拓扑分量和符号

Inkang Kim, Xueyuan Wan

Comments: 80 pages, 6 figures, 2 tables. Corrected some expressions and typos

Subjects: Geometric Topology (math.GT) ; Representation Theory (math.RT)

[19] arXiv:2508.05120 (cross-list from math.GT) [cn-pdf, pdf, other]

Title: Turaev-Viro invariant from the modular double of $\mathrm {U}_{q}\mathfrak{sl}(2;\mathbb R)$ Show Chinese title

Title: 从$\mathrm {U}_{q}\mathfrak{sl}(2;\mathbb R)$的模双代数的图雅尔-维罗不变量

Tianyue Liu, Shuang Ming, Xin Sun, Baojun Wu, Tian Yang

Comments: 108 pages, 26 figures. arXiv admin note: text overlap with arXiv:2308.06643, arXiv:2105.08805 by other authors

Subjects: Geometric Topology (math.GT) ; Mathematical Physics (math-ph) ; Probability (math.PR) ; Quantum Algebra (math.QA)

[20] arXiv:2508.05146 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Liftable braids and the coloured braid groupoid Show Chinese title

Title: 可提升的辫子和着色辫子范畴

Joan Licata, Vera Vértesi

Comments: 22 pages, 13 figures

Subjects: Geometric Topology (math.GT) ; Combinatorics (math.CO) ; Group Theory (math.GR) ; Representation Theory (math.RT)

[21] arXiv:2508.05555 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: From arcs to curves: quadratic growth of 1-systems Show Chinese title

Title: 从弧到曲线：1-系统二次增长

Tarik Aougab, Jonah Gaster

Comments: 21 pages, 14 figures, comments welcome!

Subjects: Geometric Topology (math.GT) ; Combinatorics (math.CO)

[22] arXiv:2508.05605 (cross-list from math.GT) [cn-pdf, pdf, other]

Title: Annular SL(2) and SL(3) web algebras Show Chinese title

Title: 环形SL(2)和SL(3)网络代数

Rostislav Akhmechet, Mikhail Khovanov, Melissa Zhang

Comments: 54 pages, many figures

Subjects: Geometric Topology (math.GT) ; Quantum Algebra (math.QA)

[23] arXiv:2508.05756 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: A note on the singularity conjecture for infinite covolume discrete subgroups Show Chinese title

Title: 关于无限余体积离散子群的奇异性猜想的一篇注记

Dongryul M. Kim, Andrew Zimmer

Comments: v1: 16 pages. Comments welcome!

Subjects: Geometric Topology (math.GT) ; Dynamical Systems (math.DS) ; Group Theory (math.GR) ; Probability (math.PR)

[24] arXiv:2508.06395 (cross-list from math.GT) [cn-pdf, pdf, other]

Title: Slope detection, taut foliations, and the relative L-space conjecture Show Chinese title

Title: 斜率检测，紧致叶状结构，以及相对L空间猜想

Steven Boyer, Cameron McA. Gordon, Ying Hu

Comments: There is an error in the proof of Theorem 5.7 in the previous version

Subjects: Geometric Topology (math.GT)

[25] arXiv:2508.06679 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Geometric models and asymptotic dimension for infinite-type surface mapping class groups Show Chinese title

Title: 几何模型和无限类型曲面映射类群的渐近维数

Michael C. Kopreski, George Shaji

Comments: 18 pages, 3 figures

Subjects: Geometric Topology (math.GT) ; General Topology (math.GN) ; Group Theory (math.GR)

[26] arXiv:2508.07303 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Rigidity of highly twisted plat diagrams Show Chinese title

Title: 高度扭曲的平面图的刚性

Nir Lazarovich, Yoav Moriah, Tali Pinsky, Jessica S. Purcell

Comments: 36 pages, 13 figures

Subjects: Geometric Topology (math.GT)

[27] arXiv:2508.07504 (cross-list from math.GT) [cn-pdf, pdf, other]

Title: Homotopy classification of $4$-manifolds with $3$-manifold fundamental group Show Chinese title

Title: 同伦分类具有$3$-流形基本群的$4$-流形

Jonathan Hillman, Daniel Kasprowski, Mark Powell, Arunima Ray

Comments: 64 pages, 2 figures

Subjects: Geometric Topology (math.GT)

[28] arXiv:2508.07732 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Rectangular diagrams of foliations Show Chinese title

Title: 叶层的矩形图

Mikhail Chernavskikh, Ivan Dynnikov

Comments: 40 pages, 25 figures

Subjects: Geometric Topology (math.GT)

[29] arXiv:2508.08102 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Knot primality: knot Floer homology, metacyclic representations and twisted homology Show Chinese title

Title: 纽结素性：纽结弗洛尔同调，次循环表示和扭曲同调

Samantha Allen, Charles Livingston

Comments: 14 pages

Subjects: Geometric Topology (math.GT)

[30] arXiv:2508.08539 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Distinguishing Curve Types and Designer Metrics Show Chinese title

Title: 区分曲线类型和设计指标

Ara Basmajian, Sayantika Mondal

Subjects: Geometric Topology (math.GT)

[31] arXiv:2508.08897 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Minimising length of closed billiard trajectories on hyperbolic polygons Show Chinese title

Title: 最小化双曲多边形上的闭合弹道轨迹的长度

John Parker, Manvendra Somvanshi

Comments: 11 pages, 3 figures

Subjects: Geometric Topology (math.GT)

[32] arXiv:2508.09421 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Algebraic Mapping Class Group Rigidity Show Chinese title

Title: 代数映射类群刚性

Seong Youn Kim

Comments: 18 pages, 3 figures

Subjects: Geometric Topology (math.GT)

[33] arXiv:2508.09807 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Brownian motion and orbit counting of Kleinian groups Show Chinese title

Title: 布朗运动与克莱因群的轨道计数

Yanlong Hao, Beibei Liu

Comments: 28 pages

Subjects: Geometric Topology (math.GT) ; Group Theory (math.GR) ; Probability (math.PR)

[34] arXiv:2508.09842 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Branched Covers of Open Manifolds Show Chinese title

Title: 开流形的分支覆盖

Mark Hughes, Alexandra Kjuchukova, Maggie Miller

Comments: 20 pages, 12 images, 1 graphic, 1 footnote

Subjects: Geometric Topology (math.GT)

[35] arXiv:2508.10279 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: A supergroup series for knot complements Show Chinese title

Title: 纽结补的超群序列

John Chae

Comments: 40 pages, 9 figures

Subjects: Geometric Topology (math.GT) ; High Energy Physics - Theory (hep-th) ; Mathematical Physics (math-ph) ; Quantum Algebra (math.QA)

[36] arXiv:2508.10410 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: The bracket polynomial of the Celtic link shadow $CK_4^{2n}$ Show Chinese title

Title: 凯尔特 link 阴影的括号多项式$CK_4^{2n}$

Franck Ramaharo

Comments: 16 pages, 10 figures, 2 tables, 2 OEIS A-numbers

Subjects: Geometric Topology (math.GT) ; Combinatorics (math.CO)

[37] arXiv:2508.10499 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Stably exotic 4-manifolds Show Chinese title

Title: 稳定异样的4流形

Daniel Kasprowski, Mark Powell

Comments: 19 pages

Subjects: Geometric Topology (math.GT)

[38] arXiv:2508.11065 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: The arc complex is not quasi-isometric to the sphere complex Show Chinese title

Title: 弧复形与球面复形不是拟等距的

Tarik Aougab, Marissa Loving

Comments: 8 pages

Subjects: Geometric Topology (math.GT) ; Group Theory (math.GR)

[39] arXiv:2508.11104 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Isotopy versus equivariant isotopy in dimensions three and higher Show Chinese title

Title: 同胚与等变同胚在三维及更高维中的区别

Trent Lucas

Comments: v2:Minor corrections and clarifications. 44 pages, 9 figures. Comments welcome!

Subjects: Geometric Topology (math.GT)

[40] arXiv:2508.11373 (cross-list from math.GT) [cn-pdf, pdf, other]

Title: Efficient calculations of $S$-invariants for links Show Chinese title

Title: 链接的$S$不变量的有效计算

Dirk Schuetz

Comments: 13 pages, 7 figures

Subjects: Geometric Topology (math.GT)

[41] arXiv:2508.12203 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: The ${\rm SL}(2,\mathbb{C})$-character variety of $8_{18}$ Show Chinese title

Title: ${\rm SL}(2,\mathbb{C})$-特征簇的$8_{18}$

Haimiao Chen

Comments: 30 pages, 2 figures. Final version, to appear in BMMSS

Subjects: Geometric Topology (math.GT)

[42] arXiv:2508.12272 (cross-list from math.GT) [cn-pdf, pdf, other]

Title: Lipshitz--Sarkar stable homotopy type for certain planar trivalent graphs with perfect matchings Show Chinese title

Title: Lipshitz--Sarkar 稳定同伦类型对于某些具有完美匹配的平面三价图

Nilangshu Bhattacharyya

Comments: 47 pages, 44 figures

Subjects: Geometric Topology (math.GT)

[43] arXiv:2508.12874 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: The Euler Class and Flux Homomorphisms under Non-Orientability Show Chinese title

Title: 欧拉类与非可定向下的通量同态

KyeongRo Kim, Shuhei Maruyama

Subjects: Geometric Topology (math.GT)

[44] arXiv:2508.13331 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Psyquandle Brackets Show Chinese title

Title: 心理环括号

Sam Nelson, Natsumi Oyamaguchi

Comments: 14 pages

Subjects: Geometric Topology (math.GT) ; Quantum Algebra (math.QA)

[45] arXiv:2508.13369 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Dehn surgery functions are never injective Show Chinese title

Title: 德恩手术函数从不是单射的

Kyle Hayden, Lisa Piccirillo, Laura Wakelin

Comments: 25 pages, 20 figures

Subjects: Geometric Topology (math.GT)

[46] arXiv:2508.13464 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Counting hyperbolic 4-manifolds with vanishing Seiberg-Witten invariants Show Chinese title

Title: 计数具有零Seiberg-Witten不变量的双曲4-流形

Kaixu Zhang

Comments: 14 pages

Subjects: Geometric Topology (math.GT)

[47] arXiv:2508.14038 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: On Topology of the Infinite-Dimensional Space of Fibrations Show Chinese title

Title: 论纤维映射无限维空间的拓扑

Ziqi Fang

Comments: 128 pages. Revised version of PhD thesis (2024)

Subjects: Geometric Topology (math.GT) ; Algebraic Topology (math.AT) ; Differential Geometry (math.DG)

[48] arXiv:2508.14244 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Volumes of end-periodic mapping tori Show Chinese title

Title: 端周期映射环面的体积

Marissa Loving

Comments: 31 pages, 33 figures; This expository paper builds on lecture notes from a minicourse entitled, "Infinite-type surfaces, end-periodic homeomorphisms, and the geometry of 3-manifolds", which was given by the author as part of the 2023 Riverside Workshop on Geometric Group Theory

Subjects: Geometric Topology (math.GT) ; Dynamical Systems (math.DS)

[49] arXiv:2508.14398 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Computing Khovanov homology of tangles Show Chinese title

Title: 计算辫子的Khovanov同调

Li Shen, Jian Liu, Guo-Wei Wei

Subjects: Geometric Topology (math.GT) ; General Topology (math.GN)

[50] arXiv:2508.14404 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Khovanov homology of tangles: algorithm and computation Show Chinese title

Title: 塔伦的Khovanov同调：算法与计算

Li Shen, Jian Liu, Guo-Wei Wei

Subjects: Geometric Topology (math.GT)