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Fiber detection for state surfaces

Futer, D
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Journal Article
Date
2013-07-18
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math.GT
 math.GT
 57M25, 57M27, 57M50
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http://hdl.handle.net/20.500.12613/5949
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1201.1643v2.pdf
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10.2140/agt.2013.13.2799
Abstract
Every Kauffman state σ of a link diagram D.K/ naturally defines a state surface Sσ whose boundary is K. For a homogeneous state σ, we show that K is a fibered link with fiber surface Sσ if and only if an associated graph G′ σ 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 the obstructions to certain state surfaces being fibers for K. This provides a dramatically simpler proof of a theorem of the author with Kalfagianni and Purcell.
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Mathematical Sciences Publishers
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Algebraic and Geometric Topology
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