Homology cobordisms with no 3-handles

Homology cobordisms are a special type of manifold which are relevant to a variety of areas in geometric topology, including knot theory and triangulability. We study the behavior of a variety of invariants under a particular family of four-dimensional homology cobordisms, including Floer homology and character varieties. This is joint work with Ali Daemi, Shea Vela-Vick, and Mike Wong