Stabilization for mapping class groups of 3-manifolds

By A. Hatcher, Nathalie Wahl. 2007

173 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a1108da9a97265d2ad6a989967d855ea694a1d82

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Homological stability for mapping class groups of surfaces (2010, background): “…the group, so that the stabilizers of simplices are previous groups in the sequence—the spectral sequence for the action of the group on the simplicial complex decomposes then the homology of the group in terms of the homology of the stabilizers of the action, making an inductive argument possible.”
Resolutions of moduli spaces and homological stability (2009, background): “ry [8, Theorem 5], with a slightly worse (in constant term, not in slope) range than we give here. Stability of the braid groups βn is due to Arnol’d [1]. The stability of βn≀Gappears in Hatcher–Wahl [11]. The braided products of a space Xdo not seem to have been studied. 4.4. Adding and removing pu”
FI_W-modules and stability criteria for representations of the classical Weyl groups (2013, result): “Their work complements the results of Hatcher [Hat95] for G ∼= Z and extends results of Hatcher–Wahl [HW10] for several important classes of groups G coming from low-dimensional topology.”
Stability in the homology of congruence subgroups (2012, unknown): “, [12]).”