#### Volume 15, issue 3 (2015)

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Mod $p$ decompositions of the loop spaces of compact symmetric spaces

### Shizuo Kaji, Akihiro Ohsita and Stephen Theriault

Algebraic & Geometric Topology 15 (2015) 1771–1811
##### Abstract

We give $p$–local homotopy decompositions of the loop spaces of compact, simply connected symmetric spaces for quasi-regular primes. The factors are spheres, sphere bundles over spheres and their loop spaces. As an application, upper bounds for the homotopy exponents are determined.

##### Keywords
homotopy decomposition, symmetric space, homotopy exponent
##### Mathematical Subject Classification 2010
Primary: 55P15, 55P40
Secondary: 57T20
##### Publication
Received: 4 July 2014
Revised: 25 September 2014
Accepted: 25 September 2014
Published: 19 June 2015
##### Authors
 Shizuo Kaji Department of Mathematical Sciences Faculty of Science Yamaguchi University 1677-1, Yoshida Yamaguchi 753-8512 Japan Akihiro Ohsita Faculty of Economics Osaka University of Economics 2-2-8 Osumi Hiogashiyodogawa Ward Osaka 533-8533 Japan Stephen Theriault School of Mathematics University of Southampton Southampton SO17 BJ UK