Algebraic & Geometric Topology

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

Shizuo Kaji, Akihiro Ohsita, and Stephen Theriault

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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.

Article information

Algebr. Geom. Topol., Volume 15, Number 3 (2015), 1771-1811.

Received: 4 July 2014
Revised: 25 September 2014
Accepted: 25 September 2014
First available in Project Euclid: 16 November 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55P15: Classification of homotopy type 55P40: Suspensions
Secondary: 57T20: Homotopy groups of topological groups and homogeneous spaces

homotopy decomposition symmetric space homotopy exponent


Kaji, Shizuo; Ohsita, Akihiro; Theriault, Stephen. Mod $p$ decompositions of the loop spaces of compact symmetric spaces. Algebr. Geom. Topol. 15 (2015), no. 3, 1771--1811. doi:10.2140/agt.2015.15.1771.

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