Mod p decompositions of the loop spaces of compact symmetric spaces

TL;DR

This paper provides p-local homotopy decompositions of loop spaces of compact symmetric spaces, identifying their factors as spheres and sphere bundles, and uses these results to bound homotopy exponents.

Contribution

It introduces explicit p-local decompositions of loop spaces for symmetric spaces, advancing understanding of their homotopy structure at quasi-regular primes.

Findings

Decomposition of loop spaces into spheres and sphere bundles

Determination of upper bounds for homotopy exponents

Application to symmetric spaces at quasi-regular primes

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.