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

p–Primary homotopy decompositions of looped Stiefel manifolds and their exponents
p–Primary homotopy decompositions of looped Stiefel manifolds and their exponents
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.
stiefel manifold, homotopy decomposition, homotopy exponent
1472-2747
1089-1106
Beben, Piotr
a74d3e1f-52e0-4dc6-8f20-9c1628a20d2b
Beben, Piotr
a74d3e1f-52e0-4dc6-8f20-9c1628a20d2b

Beben, Piotr (2010) p–Primary homotopy decompositions of looped Stiefel manifolds and their exponents. Algebraic & Geometric Topology, 10 (2), 1089-1106. (doi:10.2140/agt.2010.10.1089).

Record type: Article

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.

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More information

Published date: 2010
Keywords: stiefel manifold, homotopy decomposition, homotopy exponent
Organisations: Mathematical Sciences

Identifiers

Local EPrints ID: 365622
URI: http://eprints.soton.ac.uk/id/eprint/365622
ISSN: 1472-2747
PURE UUID: a73ffb2b-2f73-4e51-8b6b-cd84999a13a4

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Date deposited: 10 Jun 2014 15:24
Last modified: 16 Jul 2019 21:03

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