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State surfaces in knot complements
by
Jessica S Purcell
Brigham Young University
Coauthors: David Futer, Efstratia Kalfagianni
In the last decade, there have been several breakthroughs in hyperbolic geometry and 3-manifold topology. One goal in the research community is to use these new results to shed light on related problems, for example problems in knot and link theory. In this talk, we will describe some of our work in this direction. We determine geometric information on incompressible spanning surfaces in a large class of knot and link diagrams. Study of the geometric properties of these surfaces allows us to detect fibers and bound volumes, and relate them to certain coefficients of the Jones polynomial. This is joint with David Futer and Efstratia Kalfagianni.
Date received: November 18, 2012
Copyright © 2012 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbfw-27.