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Homology stability for symmetric diffeomorphism and mapping class groups

Published online by Cambridge University Press:  02 December 2015

ULRIKE TILLMANN*
Affiliation:
Mathematical Institute, Oxford University, Andrew Wiles Building, Oxford, OX2 6GG. e-mail: Ulrike.Tillmann@maths.ox.ac.uk

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.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 2015 

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