We prove that the homology of the mapping class group of any 3-manifold
stabilizes under connected sum and boundary connected sum with an arbitrary
3-manifold when both manifolds are compact and orientable. The stabilization
also holds for the quotient group by twists along spheres and disks, and
includes as particular cases homological stability for symmetric automorphisms
of free groups, automorphisms of certain free products, and handlebody mapping
class groups. Our methods also apply to manifolds of other dimensions in the
case of stabilization by punctures.Comment: v4: improvements in the exposition as well as improvements in the
main combinatorial theorem in the paper, concerning complexes built from
join
