Mapping class groups of 3-manifolds

In this talk I will survey foundational results in the study of mapping class groups of 3- manifolds. We will focus on Brendle-Broaddus-Putman’s recent work on the mapping class group of connected sums of S^1 x S^2, and how this result fits into the larger story. If time permits, we will work to understand Brendle-Broaddus-Putman’s new proof that twists about non-separating spheres in a 3-manifold are often non-trivial.