p–Primary homotopy decompositions of looped Stiefel manifolds and their exponents

Let $p$ be an odd prime, and fix integers $m$ and $n$ such that $0 < m < n \leq (p - 1) (p - 2)$ . We give a $p$ –local homotopy decomposition for the loop space of the complex Stiefel manifold $W_{n, m}$ . Similar decompositions are given for the loop space of the real and symplectic Stiefel manifolds. As an application of these decompositions, we compute upper bounds for the $p$ –exponent of $W_{n, m}$ . Upper bounds for $p$ –exponents in the stable range $2 m < n$ and $0 < m \leq (p - 1) (p - 2)$ are computed as well.

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Keywords

Stiefel manifold, homotopy decomposition, homotopy exponent

Mathematical Subject Classification 2000

Primary: 55P15, 55P35, 55Q05, 57T20

References

Publication

Received: 10 February 2009

Revised: 7 January 2010

Accepted: 7 January 2010

Published: 23 May 2010

Authors

Piotr Beben
Department of Mathematics National University of Singapore Block S17 (SOC1) 10, Lower Kent Ridge Road Singapore 119076

Volume 10, issue 2 (2010)

Piotr Beben

Abstract