- This event has passed.

# Algebra/Topology Seminar – Eamonn Tweedy (Widener University)

## April 14, 2021 @ 11:00 am - 12:00 pm

**Title:** The co-rank of three-dimensional homology handlebody groups

**Abstract: **A group G is called *very large* if G has a non-abelian free quotient. We examine the question of which three-manifolds have very large fundamental group. This question is especially subtle for a three-dimensional homology handlebody of genus g, since the fundamental group of such a manifold is very close to being a free group of rank g. We show that Thurston’s famous “tripus” manifold, a homology handlebody of genus 2, has fundamental group which is not very large. It is still unknown whether every homology handlebody of genus at least 3 must have very large fundamental group. However, we prove that for each g, there exists a homology handlebody of genus g whose fundamental group contains a free quotient of rank roughly half of g, but no greater. This project was joint work with Shelly Harvey.