Mod p decompositions of the loop spaces of compact symmetric spaces

Kaji, Shizuo; Ohsita, Akihiro; Theriault, Stephen

doi:10.2140/agt.2015.15.1771

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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

DOI: 10.2140/agt.2015.15.1771

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

Volume 15, issue 3 (2015)