Volume 15, issue 3 (2015)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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
References
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