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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
$p$–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 < m < n (p 1)(p 2). 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 (p 1)(p 2) are computed as well.

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