## Algebraic & Geometric Topology

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

Piotr Beben

#### 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 $Wn,m$. 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 $Wn,m$. Upper bounds for $p$–exponents in the stable range $2m and $0 are computed as well.

#### Article information

Source
Algebr. Geom. Topol., Volume 10, Number 2 (2010), 1089-1106.

Dates
Revised: 7 January 2010
Accepted: 7 January 2010
First available in Project Euclid: 19 December 2017

https://projecteuclid.org/euclid.agt/1513715127

Digital Object Identifier
doi:10.2140/agt.2010.10.1089

Mathematical Reviews number (MathSciNet)
MR2653057

Zentralblatt MATH identifier
1200.55010

#### Citation

Beben, Piotr. $p$–Primary homotopy decompositions of looped Stiefel manifolds and their exponents. Algebr. Geom. Topol. 10 (2010), no. 2, 1089--1106. doi:10.2140/agt.2010.10.1089. https://projecteuclid.org/euclid.agt/1513715127

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