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