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Equivariant scanning and stable splittings of configuration spaces

We give a definition of the scanning map for configuration spaces that is equivariant under the action of the diffeomorphism group of the underlying manifold. We use this to extend the Bödigheimer-Madsen result for the stable splittings of the Borel constructions of certain mapping spaces from compact Lie group actions to all smooth actions. Moreover, we construct a stable splitting of configuration spaces which is equivariant under smooth group actions, completing a zig-zag of equivariant stable homotopy equivalences between mapping spaces and certain wedge sums of spaces. Finally we generalise these results to configuration spaces with twisted labels (labels in a fibre bundle subject to certain conditions) and extend the Bödigheimer-Madsen result to more mapping spaces.

Identiferoai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:604366
Date January 2012
CreatorsManthorpe, Richard
ContributorsTillmann, Ulrike
PublisherUniversity of Oxford
Source SetsEthos UK
Detected LanguageEnglish
TypeElectronic Thesis or Dissertation
Sourcehttp://ora.ox.ac.uk/objects/uuid:b44e2382-487d-4e70-aeab-3c2303846dcb

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