English

Simple loops on 2-bridge spheres in 2-bridge link complements

Geometric Topology 2015-03-19 v3 Group Theory

Abstract

The purpose of this note is to announce complete answers to the following questions. (1) For an essential simple loop on a 2-bridge sphere in a 2-bridge link complement, when is it null-homotopic in the link complement? (2) For two distinct essential simple loops on a 2-bridge sphere in a 2-bridge link complement, when are they homotopic in the link complement? We also announce applications of these results to character varieties and McShane's identity.

Cite

@article{arxiv.1104.3462,
  title  = {Simple loops on 2-bridge spheres in 2-bridge link complements},
  author = {Donghi Lee and Makoto Sakuma},
  journal= {arXiv preprint arXiv:1104.3462},
  year   = {2015}
}

Comments

19 pages, 6 figures; Theorem 2.6 revised; to appear in Electron. Res. Announc. Math. Sci

R2 v1 2026-06-21T17:55:32.563Z