#### Volume 10, issue 2 (2010)

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

### Piotr Beben

Algebraic & Geometric Topology 10 (2010) 1089–1106
##### Abstract

Let $p$ be an odd prime, and fix integers $m$ and $n$ such that $0. 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 $2m and $0 are computed as well.

##### Keywords
Stiefel manifold, homotopy decomposition, homotopy exponent
##### Mathematical Subject Classification 2000
Primary: 55P15, 55P35, 55Q05, 57T20