Retracts in free groups

Abstract: A subgroup R of a group G is said to be a retract of G if there is a homomorphism r : G → R that restricts to the identity on R. I will talk about retracts in free groups. In particular, I will discuss the following question raised by Bergman: Let F be a free group of finite rank and let R be a retract of F. Is it H ∩ R is a retract of H for every finitely generated subgroup H of F?

This talk is based on a joint work with Slobodan Tanushevski and Pavel Zalesskii.

algebraic topologydifferential geometrygeneral topologygroup theorygeometric topology

Audience: researchers in the topic

Ohio State Topology and Geometric Group Theory Seminar

Series comments: https://sites.google.com/view/topoandggt