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GTC 2019: Speaker: Nathan Dunfield

Boyd Graduate Studies Bldg., Room 328

Title of talk: An SL(2, R) Casson-Lin invariant and applications

Abstract: When M is the exterior of a knot K in the 3-sphere, Lin showed that the signature of K can be viewed as a Casson-style signed count of the SU(2) representations of the fundamental group of M where the meridian has trace 0. This was later generalized to the fact that signature function of K on the unit circle counts SU(2) representations as a function of the trace of the meridan. I will define the SL(2,R) analog of these Casson-Lin invariants, and explain how it interacts with the original SU(2) version via a new kind of smooth resolution of the real points of certain SL(2, C)-character varieties in which both kinds of representations live. I will use the new invariant to study leftorderability of Dehn fillings on M using the translation extension locus I introduced with Marc Culler, and also give a new proof of a recent theorem of Gordons on parabolic SL(2,R) representations of two-bridge knot groups. This is joint work with Jake Rasmussen.





Conference Organizers:

  • David Gay
  • Gordana Matic
  • Rachel Roberts
  • contact us

The University of Georgia has hosted the annual Georgia Topology Conference since 1961.  You can find information on previous conferences, including the octennial Georgia International Topology Conferences, here.

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