Geometry and Topology seminar
Speaker: Dr. Sudipta Ghosh, University of Notre Dame
Host: Sandip Singh
Title: Rational homology spheres and SU(2)-SL(2,C) representations
Time, day and date: 5:30:00 PM - 6:30:00 PM, Thursday, March 26
Venue: Online (Google Meet: https://meet.google.com/jzy-kqch-nzy)
Abstract: The Poincaré Conjecture, proved by Perelman, states that every closed, connected three-manifold other than S³ has nontrivial fundamental group. A related question, Problem 3.105(A) in Kirby’s list, asks whether any three-manifold other than S³ admits a nontrivial homomorphism from π₁(Y) to SU(2); this problem remains open. Using instanton Floer homology, Zentner showed that for integer homology spheres, the analogous statement holds when SU(2) is replaced by SL(2,C). In this talk, I will discuss recent progress on the existence of irreducible SL(2,C) and SU(2) representations for rational homology spheres. Some of these results are joint with Steven Sivek and Raphael Zentner, others with Mike Miller Eismeier, and others with Zhenkun Li and Juanita Pinzón-Caicedo.