Wednesday, May 22 2019, 9am Boyd Graduate Studies Bldg., Room 328 http://research.franklin.uga.edu/topology/2019GTC 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.
