Splittings of knot groups
Geometric Topology
2013-08-30 v1 Group Theory
Abstract
Let K be a knot of genus g. If K is fibered, then it is well known that the knot group pi(K) splits only over a free group of rank 2g. We show that if K is not fibered, then pi(K) splits over non-free groups of arbitrarily large rank. Furthermore, if K is not fibered, then pi(K) splits over every free group of rank at least 2g. However, pi(K) cannot split over a group of rank less than 2g. The last statement is proved using the recent results of Agol, Przytycki-Wise and Wise.
Keywords
Cite
@article{arxiv.1308.6497,
title = {Splittings of knot groups},
author = {Stefan Friedl and Daniel S. Silver and Susan G. Williams},
journal= {arXiv preprint arXiv:1308.6497},
year = {2013}
}
Comments
28 pages, 2 figures