Homomorphisms to 3-manifold groups

Abstract

We prove foundational results about the set of homomorphisms from a finitely generated group to the collection of all fundamental groups of compact 3-manifolds and answer questions of Reid-Wang-Zhou and Agol-Liu.

50 pages. v2: Minor changes to introduction, and fixed some typos. Results remain unchanged. v3: 55 pages. Substantial rewrite for clarity, with details added and corrections made