We show that the homology of the mapping class group of any compact, orientable 3-manifold stabilizes under connected sum and boundary connected sum with any another 3-manifold. The stabilization also holds for certain quotient groups, and includes as particular cases homological stability for symmetric automorphisms of free groups, automorphisms of certain free products, and handlebody mapping class groups. (Joint work with Allen Hatcher) |
Phone: 541-346-4705 Fax: 541-346-0987