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Splitting ℂP∞ and Bℤ/pn into Thom spectra

Published online by Cambridge University Press:  28 June 2011

Brayton Gray  and
Nigel Ray
Brayton Gray
Affiliation:
University of Illinois at Chicago, Box 4348, Chicago IL 60680, U.S.A.
Nigel Ray
Affiliation:
The University, Manchester M13 9PL, England
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Extract

In recent years, much work in algebraic topology has been devoted to stable splitting phenomena. Often the existence of these splittings has first been detected at the cohomological level in terms of modules over the Steenrod algebra.

For example, W. Richter has exhibited a decomposition of ΩSU(n) of the form

(see [7]). Not only were cohomology calculations the initial evidence for this situation, but they further suggested that each summand Gk might be the Thom complex of a suitable k-plane complex vector bundle. This possibility was also verified by Mitchell.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 106 , Issue 2 , September 1989 , pp. 263 - 271
Copyright
Copyright © Cambridge Philosophical Society 1989

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