Volume 13, issue 5 (2013)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Fiber detection for state surfaces

David Futer

Algebraic & Geometric Topology 13 (2013) 2799–2807
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 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.

Keywords
adequate knot, homogeneous knot, spanning surface, fibration, Jones polynomial
Mathematical Subject Classification 2010
Primary: 57M25, 57M27, 57M50
References
Publication
Received: 3 May 2012
Revised: 27 March 2013
Accepted: 15 April 2013
Published: 18 July 2013
Authors
David Futer
Department of Mathematics
Temple University
Philadelphia, PA 19122
USA
http://math.temple.edu/~dfuter