# Homology stability for symmetric diffeomorphism and mapping class groups

@article{Tillmann2015HomologySF, title={Homology stability for symmetric diffeomorphism and mapping class groups}, author={Ulrike Tillmann}, journal={Mathematical Proceedings of the Cambridge Philosophical Society}, year={2015}, volume={160}, pages={121 - 139} }

Abstract For any smooth compact manifold W with boundary of dimension of 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.

## 11 Citations

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