Presentation length and Simon’s conjecture-Reference-Cited by-同舟云学术

Presentation length and Simon’s conjecture

Published:2011-07-12 Issue:1 Volume:25 Page:151-187
ISSN:0894-0347
Container-title:Journal of the American Mathematical Society
language:en
Short-container-title:J. Amer. Math. Soc.

Author:

Agol Ian,Liu Yi

Abstract

In this paper, we show that any knot group maps onto at most finitely many knot groups. This gives an affirmative answer to a conjecture of J. Simon. We also bound the diameter of a closed hyperbolic 3-manifold linearly in terms of the presentation length of its fundamental group, improving a result of White.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/jams/2012-25-01/S0894-0347-2011-00711-X/S0894-0347-2011-00711-X.pdf

Reference28 articles.

1. Simon’s conjecture for two-bridge knots;Boileau, Michel;Comm. Anal. Geom.,2010

2. Michel Boileau, Hyam Rubinstein, and Shicheng Wang, Finiteness of 3-manifolds associated with non-zero degree mappings, preprint, 2005, math.GT/0511541.

3. The structure of 3-manifolds with two-generated fundamental group;Boileau, Michel;Topology,2005

4. JSJ-decompositions of knot and link complements in 𝑆³;Budney, Ryan;Enseign. Math. (2),2006

5. Lattice constants and a lemma of Zagier;Cao, C.,1997

Cited by 16 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Minimality of rational knots C(2n + 1,2m,2);Journal of Knot Theory and Its Ramifications;2024-02

2. Discrete representations of finitely generated groups into PSL(2,R)${\rm PSL}(2,\mathbb {R})$;Journal of the London Mathematical Society;2023-07-28

3. Generating functions on epimorphisms between 2-bridge knot groups;Journal of Knot Theory and Its Ramifications;2021-08

4. Finiteness of nonzero degree maps between 3‐manifolds;Journal of Topology;2020-03

5. Remarks on Suzuki’s knot epimorphism number;Journal of Knot Theory and Its Ramifications;2019-08