Stabilization for mapping class groups of 3-manifolds

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.

v4: improvements in the exposition as well as improvements in the main combinatorial theorem in the paper, concerning complexes built from joins

References in corpus (3)

• The integral cohomology of the group of loops
• Erratum to ``Stabilization for the automorphisms of free groups with boundaries''
• Configuration spaces of rings and wickets

Cited by in corpus (71)

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• Topology of moduli spaces of tropical curves with marked points
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• Assembling homology classes in automorphism groups of free groups
• Stability in the homology of congruence subgroups
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• Representation stability for the cohomology of the moduli space M_g^n
• Erratum to ``Stabilization for the automorphisms of free groups with boundaries''
• A topological approach to Neutrino masses by using exotic smoothness
• On the cohomology of pure mapping class groups as FI-modules
• Non-integrality of some Steinberg modules
• Homological Stability for Diffeomorphism Groups of High Dimensional Handlebodies
• Linking forms and stabilization of diffeomorphism groups of manifolds of dimension 4n+1
• On the top dimensional cohomology groups of congruence subgroups of ${\text{SL}}_n(\mathbb{Z})$
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• Stable cohomology of $Aut(F_n)$ with bivariant twisted coefficients
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