Jesse Johnson, Hyam Rubinstein
Published 2007-01-04, updated 2011-10-28Version 4
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.
Comments: 21 pages, 4 figures. The proof of Theorem 1 has been shortened and Theorem 2 has been significantly strengthened
Thick isotopy property and the mapping class groups of Heegaard splittings
Automorphisms of the three-torus preserving a genus three Heegaard splitting
Addendum and correction to: Homology cylinders: an enlargement of the mapping class group
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