A monodromy invariant in the space of knots

Geometry Topology Seminar
Monday, September 13, 2010 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 114
Jason McGibbon – University of Massachusetts
John Etnyre
Knot contact homology (KCH) is a combinatorially defined topological invariant of smooth knots introduced by Ng. Work of Ekholm, Etnyre, Ng and Sullivan shows that KCH is the contact homology of the unit conormal lift of the knot. In this talk we describe a monodromy result for knot contact homology,namely that associated to a path of knots there is a connecting homomorphism which is invariant under homotopy. The proof of this result suggests a conjectural interpretation for KCH via open strings, which we will describe.