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arXiv · 1510.07564

Homology stability for symmetric diffeomorphism and mapping class groups

Ulrike Tillmann
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Abstract

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.

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Ulrike Tillmann. 2015-10-26. Homology stability for symmetric diffeomorphism and mapping class groups. https://doi.org/10.1017/s0305004115000638

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