An SL_2(R) Casson-Lin invariant

An SL_2(R) Casson-Lin invariant

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Jacob Rasmussen, University of Cambridge and IAS

Zoom link:https://princeton.zoom.us/j/453512481?pwd=OHZ5TUJvK2trVVlUVmJLZkhIRHFDUT09

 

In the early 90's, X.S. Lin defined a Casson-type invariant of knots in S^3 by counting representations pi_1(S^3-K)-> SU(2) with fixed holonomy around the meridian. This invariant was subsequently shown to be equivalent to the Levine-Tristram signature of K. I'll describe a similar construction, using representations to SL_2(R) and discuss some applications and connections to other known invariants.

This is joint work with Nathan Dunfield.