Fiber detection for state surfaces

Futer, David¹

¹Department of Mathematics, Temple University, Philadelphia, PA 19122, USA

Algebraic and Geometric Topology, Tome 13 (2013) no. 5, pp. 2799-2807

Résumé

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 Gσ′ 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.

Détail

DOI : 10.2140/agt.2013.13.2799

Classification : 57M25, 57M27, 57M50
Keywords: adequate knot, homogeneous knot, spanning surface, fibration, Jones polynomial

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