Algebraic & Geometric Topology

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

Piotr Beben

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Abstract

Let p be an odd prime, and fix integers m and n such that 0<m<n(p1)(p2). 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<n and 0<m(p1)(p2) are computed as well.

Article information

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

Dates
Received: 10 February 2009
Revised: 7 January 2010
Accepted: 7 January 2010
First available in Project Euclid: 19 December 2017

Permanent link to this document
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

Subjects
Primary: 55P15: Classification of homotopy type 55P35: Loop spaces 55Q05: Homotopy groups, general; sets of homotopy classes 57T20: Homotopy groups of topological groups and homogeneous spaces

Keywords
Stiefel manifold homotopy decomposition homotopy exponent

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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References

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