# 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}
}
• U. Tillmann
• Published 26 October 2015
• Mathematics
• Mathematical Proceedings of the Cambridge Philosophical Society
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.
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