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Title: Equivariant scanning and stable splittings of configuration spaces
Author: Manthorpe, Richard
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2012
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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.
Supervisor: Tillmann, Ulrike Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Algebraic topology ; scanning map ; stable splittings ; configuration spaces ; equivariant stable homotopy ; infinite loop spaces