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arXiv · 1201.1643

Fiber detection for state surfaces

David Futer
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Abstract

Every Kauffman state σof a link diagram D(K) naturally defines a state surface S_σwhose boundary is K. For a homogeneous state σ, we show that K is a fibered link with fiber surface S_σif and only if an associated graph G'_σis 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].

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David Futer. 2013-04-16. Fiber detection for state surfaces. https://doi.org/10.2140/agt.2013.13.2799

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