Notes on the isotopy finiteness
英文摘要：
This is the less official, English version of the proof of the fact that every closed atoroidal 3-manifold carries finitely many isotopy classes of tight contact structures.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
相关论文
通过接触几何研究三维流形上Anosov流的有限性
On the Finiteness of Anosov flows on $3$-manifolds via Contact Geometry
Leibniz University Hannover（汉诺威莱布尼茨大学）；Nantes Université（南特大学）
该论文通过接触几何证明闭双曲三维流形上Anosov流模同痕轨道等价类数量有限，还给出其数量显式界，并控制非双曲三维流形上Anosov流的动力学。
math.DSmath.GTmath.SG
伪Anosov流的奇异轨道的有限性
Finiteness of singular orbits of pseudo-Anosov flows
Princeton University（普林斯顿大学）
该研究证明闭合无环3维流形上伪Anosov流的奇异轨道对应的纽结同痕类数量有限，为相关几何拓扑问题提供了关键结论。
math.DSmath.GT
A note on the Legendrian isotopy problem
This paper has been withdrawn by the authors, due to a mistake pointed out by Lenny Ng and Josh Sabloff.
math.GT
A note on Kneser-Haken finiteness
Kneser-Haken Finiteness asserts that for each compact 3-manifold M there is an integer c(M) such that any collection of k>c(M) closed, essential, 2-sided surfaces in M must contain parallel elements. We show here that if M is closed then twice the number of tetrahedra in a (pseudo)-triangulation of M suffices for c(M).
math.GT
Note on the canonical genus of a knot
We show that every canonical Seifert surface is (up to isotopy) given by a knot diagram in which the (open) Seifert disks are pairwise disjoint.
math.GT
曲面Dehn广群的典范商的有限性
Finiteness of canonical quotients of Dehn quandles of surfaces
本文研究闭可定向曲面Dehn广群的典范商有限性，刻画其2-广群，确定n-广群有限的n值，计算最小非平凡商大小，还证明Artin广群对合商为Coxeter广群并确定辫子广群最小非平凡商。
math.GRmath.GTmath.QA
更多相关论文收起更多论文
Wall's finiteness obstruction
The purpose of this note is to give a self contained description of Walls finiteness obstruction.
math.ATmath.GTmath.KT
同伦与同调：5维流形中的2球面
Homotopy versus isotopy: 2-spheres in 5-manifolds
ETH Zürich（苏黎世联邦理工学院）；Lehman College, City University of New York（纽约市立大学莱曼学院）；Max-Planck-Institut für Mathematik（马克斯·普朗克数学研究所）
本文研究了5维流形中2球面的同伦与同调关系，通过Whitney移动消除二重点，证明了在特定条件下同伦等价于同调。
math.ATmath.GT
Finiteness of mapping degree sets for 3-manifolds
By constructing certain maps, this note completes the answer of the Question: For which closed orientable 3-manifold $N$, the set of mapping degrees $cD(M,N)$ is finite for any closed orientable 3-manifold $M$?
math.GT
Domination between different products and finiteness of associated semi-norms
In this note we determine all possible dominations between different products of manifolds, when none of the factors of the codomain is dominated by products. As a consequence, we determine the finiteness of every product-associated functorial semi-norm on the fundamental classes of the aforementioned products. These results give partial answers to questions of M. Gromov.
math.ATmath.GT
Free quandles and knot quandles are residually finite
In this note, residual finiteness of quandles is defined and investigated. It is proved that free quandles and knot quandles of tame knots are residually finite and Hopfian. Residual finiteness of quandles arising from residually finite groups (conjugation, core and Alexander quandles) is established. Further, residual finiteness of automorphism groups of some residually finite quandles is also discussed.
math.GT
Waldhausen's Theorem
This note is an exposition of Waldhausen's proof of Waldhausen's Theorem: the three-sphere has a single Heegaard splitting, up to isotopy, in every genus. As a necessary step we also give a sketch of the Reidemeister-Singer Theorem.
math.GT
关于纽结肥沃性的注记 II
A note on knot fertility II
该研究给出纽结(m,n)-肥沃性的障碍条件，证明了(c(K)+f,c(K)+p)-肥沃纽结的有限性，并探讨最小交叉图的Seifert圈数与拧数，推进了纽结肥沃性相关理论研究。
math.GT
