The Jones polynomial and surfaces far from fibers

The Jones polynomial and surfaces far from fibers

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David Futer, Temple University
Fine Hall 314

This talk explores relations between colored Jones polynomials and the topology of incompressible spanning surfaces in knot and link complements. 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 also show that certain coefficients of the Jones and colored Jones polynomials measure the "guts" of the surface—a measurement of how far this surface is from being a fiber in the knot complement.This is joint work with Effie Kalfagianni and Jessica Purcell.