Speaker: Sudipta Ghosh
Affiliation: University of Notre Dame
Title of Talk: Homology 2-Torsion and $\mathrm{SL}(2,\mathbb{C})$
Date: January 30, 2026
Time: 11:00:00 Hours
Venue: A-369

Abstract: Building on non-vanishing theorems of Kronheimer and Mrowka in instanton Floer homology, Zentner proved that if $Y$ is a homology $3$--sphere other than $S^{3}$, then its fundamental group admits a homomorphism to $\mathrm{SL}(2,\mathbb{C})$ with non-abelian image. In this talk, I will explain how to generalize this result to any $3$--manifold $Y$ whose first homology is $2$--torsion, other than $\#^{n}\mathbb{RP}^{3}$ for any $n$. This is joint work with Steven Sivek and Raphael Zentner.