Fiber detection for state surfaces

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].