English

Homology stability for symmetric diffeomorphism and mapping class groups

Algebraic Topology 2015-12-16 v1 Geometric Topology

Abstract

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

Keywords

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

R2 v1 2026-06-22T11:29:09.641Z