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Knot contact homology and string topology
by
Lenny Ng
Duke University
Coauthors: Kai Cieliebak, Tobias Ekholm, Janko Latschev
A natural question about knot contact homology, a knot invariant with origins in contact geometry, is what information it contains about the topology of a knot. Until recently we had only a rather minimal understanding of this. I will discuss a way to describe a key part of knot contact homology, the "cord algebra", through string topology. This allows us to interpret the cord algebra in terms of the fundamental group of the knot complement, and in particular to conclude that knot contact homology detects the unknot and (by work of Gordon and Lidman) torus knots.
Date received: April 8, 2016
Copyright © 2016 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 # cbmk-26.