This mini-course consists of 3 lectures, where I will introduce the basic theory required to study diffeomorphisms of 3-manifolds, from a topological perspective.
First I will introduce the classifying space B Diff(M) for M a 3-manifold, and Diff(M) the diffeomorphism group of M. I will survey known results on the homotopy type, and introduce tools including various decompositions of M, such as the prime decomposition, Jaco—Shalen Johannson decomposition, and geometric decomposition. I will survey Thurston’s geometrisation conjecture (proved by Perelman) and known results on the diffeomorphism groups of certain geometric manifolds (in particular Seifert-fibered manifolds). I will introduce tools such as helpful fiber sequences, locally retractile group actions, and topological posets.
This mini-course will contain background theory for my research talk during the topology conference, where I will talk about joint work with Bregman and Steinebrunner.