The Jones polynomial and highly non-fibered surfaces

David Futer, Michigan State University

Experimental evidence suggests that the volume of a hyperbolic knot or
link is coarsely determined by the coefficients near the head and tail
of its Jones polynomial. I will discuss some recent work that proves
this is indeed the case for a large family of links. In fact, the
volume estimate relies on the claim that coefficients of the Jones
polynomial detect that a particular surface is very far from being a
fiber. This is joint work with Effie Kalfagianni.