Fiber detection for state surfaces
Geometric Topology
2014-10-01 v2
Abstract
Every Kauffman state \sigma of a link diagram D(K) naturally defines a state surface S_\sigma whose boundary is K. For a homogeneous state \sigma, we show that K is a fibered link with fiber surface S_\sigma if and only if an associated graph G'_\sigma is a tree. As a corollary, it follows that for an adequate knot or link, the second and next-to-last coefficients of the Jones polynomial are obstructions to certain state surfaces being fibers for K. This provides a dramatically simpler proof of a theorem from [arXiv:1108.3370].
Keywords
Cite
@article{arxiv.1201.1643,
title = {Fiber detection for state surfaces},
author = {David Futer},
journal= {arXiv preprint arXiv:1201.1643},
year = {2014}
}
Comments
6 pages, 5 figures. v2 features minor revisions. To appear in Algebraic & Geometric Topology