Knot contact homology and string topology

Knot contact homology and string topology

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Lenny Ng, Princeton University
Fine Hall 314

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 some understanding of this, but the understanding was rather ad hoc. I will discuss a new 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. This is joint work with Kai Cieliebak, Tobias Ekholm, and Janko Latschev.