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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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510840974

Digital Object Identifier
doi:10.2140/agt.2015.15.1771

Mathematical Reviews number (MathSciNet)
MR3361150

Zentralblatt MATH identifier
1320.55005

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

Keywords
homotopy decomposition symmetric space homotopy exponent

Citation

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. https://projecteuclid.org/euclid.agt/1510840974


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