Proceedings of the American Mathematical Society

Author(s): Greg Arone
Journal: Proc. Amer. Math. Soc. 129 (2001), 1207-1211.
MSC (1991): Primary 55P35
Posted: 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.

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[C86]: M.C. Crabb, On stable splitting of $\operatorname{U}(n)$ and $\Omega \operatorname{U}(n)$ , Lecture Notes in Math. 1298 (1986), 35-53. MR 89d:55019
[CM88]: M.C. Crabb, and S.A. Mitchell, The loops on $\mathrm{U}(n)/\mathrm{O}(n)$ and $\mathrm{U}(2n)/ \mathrm{Sp}(n)$ , Math. Proc. Cambridge Philos. Soc. 104 (1988), 95-103. MR 89h:55019
[G96]: T.G. Goodwillie, Calculus III: the Taylor series of a homotopy functor, preprint, 1996.
[Mi85]: H. Miller, Stable splittings of Stiefel manifolds, Topology 24 (1985), 411-419. MR 87d:55009
[W95]: M. Weiss, Orthogonal calculus, Trans. Amer. Math. Soc. 347, Number 10 (1995), 3743-3796. [Erratum: Trans.Amer. Math. Soc. 350, Number 2 (1998), 851-855.] MR 96m:55018; MR 98f:55012

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 55P35

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: 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
Posted: October 4, 2000
Additional Notes: The author was partially supported by the NSF
Communicated by: Ralph Cohen
Copyright of article: Copyright 2000, American Mathematical Society

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