Abstract
Every Kauffman state of a link diagram naturally defines a state surface whose boundary is . For a homogeneous state , we show that is a fibered link with fiber surface if and only if an associated graph 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 .
This provides a dramatically simpler proof of a theorem of the author with Kalfagianni and Purcell.
Citation
David Futer. "Fiber detection for state surfaces." Algebr. Geom. Topol. 13 (5) 2799 - 2807, 2013. https://doi.org/10.2140/agt.2013.13.2799
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