Stabilization for mapping class groups of 3-manifolds

TY - JOUR

T1 - Stabilization for mapping class groups of 3-manifolds

AU - Wahl, Nathalie

AU - Hatcher, Allen

PY - 2010/11

Y1 - 2010/11

N2 - 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.

AB - 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.

M3 - Journal article

SN - 0012-7094

VL - 155

JO - Duke Mathematical Journal

JF - Duke Mathematical Journal

ER -