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On the cohomology of loop spaces for some Thom spaces | | Andrew Baker
; | | Date: |
3 May 2011 | | Abstract: | In this paper we identify conditions under which the cohomology $H^*(Omega
Mxi;k)$ for the loop space $Omega Mxi$ of the Thom space $Mxi$ of a
spherical fibration $xidownarrow B$ can be a polynomial ring. We use the
Eilenberg-Moore spectral sequence which has a particularly simple form when the
Euler class $e(xi)in H^n(B;k)$ vanishes, or equivalently when an orientation
class has trivial square. As a consequence of our homological calculations we
are able to show that the suspension spectrum $Sigma^inftyOmega Mxi$ has a
local splitting replacing the James splitting of $SigmaOmega Mxi$ when
$Mxi$ is a suspension. | | Source: | arXiv, 1105.0692 | | Services: | Forum | Review | PDF | Favorites | |
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