IMSc Webinar

SU(2) and SL(2,C) Representations of Rational Homology Spheres

Sudipta Ghosh

University of Notre Dame

Join Zoom Meeting
zoom.us/j/91573997114

Meeting ID: 915 7399 7114
Passcode: 492932

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.