Simple loops on 2-bridge spheres in 2-bridge link complements
arXiv:1104.3462
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.
19 pages, 6 figures; Theorem 2.6 revised; to appear in Electron. Res. Announc. Math. Sci