Mapping class groups of Heegaard splittings
arXiv:math/0701119
Abstract
The mapping class group of a Heegaard splitting is the group of automorphisms of the ambient 3-manifold that take the surface onto itself, modulo isotopies that keep the surface on itself. We characterize the mapping classes that restrict to periodic and reducible automorphisms of the surface.
21 pages, 4 figures. The proof of Theorem 1 has been shortened and Theorem 2 has been significantly strengthened