Fiber detection for state surfaces

Details Fiber detection for state surfaces Fiber detection for state surfaces

2012-01-08

arxiv.org/abs/1201.1643v1

Mathematics

Geometric Topology

6 pages, 5 figures

Scientific paper

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 generalizes a theorem from [arXiv:1108.3370], with a dramatically simpler proof.

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