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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Mitchell-Richter filtration of loops on Stiefel manifolds stably splits


Author: Greg Arone
Journal: Proc. Amer. Math. Soc. 129 (2001), 1207-1211
MSC (1991): Primary 55P35
Published electronically: October 4, 2000
MathSciNet review: 1814154
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Abstract: We prove that the Mitchell-Richter filtration of the space of loops on complex Stiefel manifolds stably splits. The result is obtained as a special case of a more general splitting theorem. Another special case is H. Miller's splitting of Stiefel manifolds. The proof uses the theory of orthogonal calculus developed by M. Weiss. The argument is inspired by an old argument of Goodwillie for a different, but closely related, general splitting result.


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Additional Information

Greg Arone
Affiliation: Department of Mathematics, The University of Chicago, Chicago, Illinois 60637
Address at time of publication: Department of Mathematics, University of Aberdeen, Aberdeen, AB24 3UE, United Kingdom
Email: arone@math.uchicago.edu, g.arone@maths.abdn.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05794-4
PII: S 0002-9939(00)05794-4
Keywords: Stable splitting, Stiefel manifolds, Weiss' calculus
Received by editor(s): June 9, 1999
Published electronically: October 4, 2000
Additional Notes: The author was partially supported by the NSF
Communicated by: Ralph Cohen
Article copyright: © Copyright 2000 American Mathematical Society