Fiber detection for state surfaces

  title={Fiber detection for state surfaces},
  author={David Futer},
Every Kauffman state of a link diagram D.K/ naturally defines a state surface S whose boundary is K . For a homogeneous state , we show that K is a fibered link with fiber surface S if and only if an associated graph G 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 . 

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