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
Abstract
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) |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| 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: | 1465-3060 |
| ISSN (Online): | 1364-0380 |
| Published Online: | 12 February 2012 |
| Related URLs: |
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