Branched covers and SU(2)-representations

Series
Geometry Topology Seminar
Time
Monday, February 10, 2025 - 2:00pm for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Juanita Pinzon-Caicedo – Notre Dame
Organizer
Jennifer Hom

The fundamental group is one of the most powerful invariants to distinguish closed three-manifolds, and the existence of non-trivial homomorphisms $\pi_1(M)\to SU(2)$ is a great way of measuring the non-triviality of a three-manifold $M$. It is known that if an integer homology 3-sphere is either Seifert fibered or toroidal, then irreducible representations do exist. In contrast, the existence of SU(2)-representations for hyperbolic homology spheres has not been completely established. With this as motivation, I will talk about partial progress made in the case of hyperbolic homology spheres realized as branched covers. This is joint work with Sudipta Ghosh and Zhenkun Li.