Juanita Pinzon Caicedo : Branched covers and SU(2)-representations.

Posted by Laura Schaposnik , part of the Departmental Colloquium.

At

Nov. 8, 2024, 3 p.m.

In

636 SEO

Abstract

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.