Stabilization for mapping class groups of 3-manifolds
Geometric Topology
2019-12-19 v4 Algebraic Topology
Abstract
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.
Cite
@article{arxiv.0709.2173,
title = {Stabilization for mapping class groups of 3-manifolds},
author = {Allen Hatcher and Nathalie Wahl},
journal= {arXiv preprint arXiv:0709.2173},
year = {2019}
}
Comments
v4: improvements in the exposition as well as improvements in the main combinatorial theorem in the paper, concerning complexes built from joins