Mapping class groups of circle bundles over a surface
with L. Chen
Michigan Math J., to appear
In this paper, we study the algebraic structure of mapping class group of 3-manifolds that fiber as a circle bundle over a surface. This mapping class group surjects to the mapping class group of the base surface. We determine when this surjection splits. In the process we relate the 3-manifold mapping class group to the Birman exact sequence.