Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 10, Number 2 (2010), 1089-1106.
$p$–Primary homotopy decompositions of looped Stiefel manifolds and their exponents
Let be an odd prime, and fix integers and such that . We give a –local homotopy decomposition for the loop space of the complex Stiefel manifold . 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 –exponent of . Upper bounds for –exponents in the stable range and are computed as well.
Algebr. Geom. Topol., Volume 10, Number 2 (2010), 1089-1106.
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
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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