The Mitchell-Richter filtration of loops on Stiefel manifolds stably splits
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- by Greg Arone
- Proc. Amer. Math. Soc. 129 (2001), 1207-1211
- DOI: https://doi.org/10.1090/S0002-9939-00-05794-4
- Published electronically: October 4, 2000
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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.References
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Bibliographic 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
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 1207-1211
- MSC (1991): Primary 55P35
- DOI: https://doi.org/10.1090/S0002-9939-00-05794-4
- MathSciNet review: 1814154