arXiv Analytics

Sign in

arXiv:1510.07564 [math.AT]AbstractReferencesReviewsResources

Homology stability for symmetric diffeomorphism and mapping class groups

Ulrike Tillmann

Published 2015-10-26Version 1

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.

Comments: to appear in Math. Proc. Cambridge Philos. Soc
Categories: math.AT, math.GT
Subjects: 55R80, 55S05, 55R40
Related articles: Most relevant | Search more
arXiv:1204.4310 [math.AT] (Published 2012-04-19)
Embeddings of braid groups into mapping class groups and their homology
arXiv:math/0406278 [math.AT] (Published 2004-06-14, updated 2005-01-27)
From mapping class groups to automorphism groups of free groups
arXiv:1709.03638 [math.AT] (Published 2017-09-12)
Quantitative representation stability over linear groups

Links

Toolbox