Homology stability for symmetric diffeomorphism and mapping class groups
Algebraic Topology
2015-12-16 v1 Geometric Topology
Abstract
For any smooth compact manifold of dimension at least two we prove that the classifying spaces of its group of diffeomorphisms which fix a set of points or embedded disks (up to permutation) satisfy homology stability. The same is true for so-called symmetric diffeomorphisms of connected sum with copies of an arbitrary compact smooth manifold of the same dimension. The analogues for mapping class groups as well as other generalisations will also be proved.
Cite
@article{arxiv.1510.07564,
title = {Homology stability for symmetric diffeomorphism and mapping class groups},
author = {Ulrike Tillmann},
journal= {arXiv preprint arXiv:1510.07564},
year = {2015}
}
Comments
to appear in Math. Proc. Cambridge Philos. Soc