On the cohomology of loop spaces for some Thom spaces

Baker, A. (2012) On the cohomology of loop spaces for some Thom spaces. Geometry and Topology, 18, pp. 59-74.

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Publisher's URL: http://nyjm.albany.edu/j/2012/18-4.html


In this paper we identify conditions under which the cohomology H*(ΩMξ;k) for the loop space ΩMξ of the Thom space Mξ of a spherical fibration ξ\downarrow B can be a polynomial ring. We use the Eilenberg-Moore spectral sequence which has a particularly simple form when the Euler class e(ξ)∈ Hn(B;k) vanishes, or equivalently when an orientation class for the Thom space has trivial square. As a consequence of our homological calculations we are able to show that the suspension spectrum Σ∞ΩMξ has a local splitting replacing the James splitting of ΣΩMξ when Mξ is a suspension.

Item Type:Articles (Other)
Glasgow Author(s) Enlighten ID:Baker, Dr Andrew
Authors: Baker, A.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Research Group:Geometry and Topology
Journal Name:Geometry and Topology
ISSN (Online):1364-0380
Published Online:12 February 2012
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