Homology stability for symmetric diffeomorphism and mapping class groups

Abstract

For any smooth compact manifold $W$ of dimension at least two we prove that the classifying spaces of its group of diffeomorphisms which fix a set of $k$ points or $k$ embedded disks (up to permutation) satisfy homology stability. The same is true for so-called symmetric diffeomorphisms of $W$ connected sum with $k$ copies of an arbitrary compact smooth manifold $Q$ of the same dimension. The analogues for mapping class groups as well as other generalisations will also be proved.

to appear in Math. Proc. Cambridge Philos. Soc

References in corpus (3)

• Homological stability for unordered configuration spaces
• Homological stability for oriented configuration spaces
• Tubular configurations: equivariant scanning and splitting

Cited by in corpus (2)

• Homological stability of topological moduli spaces
• Homological stability for moduli spaces of disconnected submanifolds, I