Guts of Surfaces and the Colored Jones Polynomial by Efstratia Kalfagianni, David Futer, Jessica Purcell (Paperback, 2012)

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Under mild diagrammatic hypotheses, we prove that the growth of the degree of the colored Jones polynomials is a boundary slope of an essential surface in the knot complement. We show that certain coefficients of the polynomial measure how far this surface is from being a fiber for the knot; in particular, the surface is a fiber if and only if a particular coefficient vanishes.