Homotopy decomposition of a suspended real toric space

TL;DR

This paper provides p-local homotopy decompositions of suspended real toric spaces at odd primes, extending known decompositions and revealing a stable rigidity property for these spaces.

Contribution

It introduces p-local homotopy decompositions for suspended real toric spaces compatible with existing decompositions, and establishes a stable rigidity property.

Findings

p-local homotopy decompositions at odd primes

Compatibility with existing decompositions for moment-angle complexes

Stable rigidity property for real toric spaces

Abstract

We give $p$-local homotopy decompositions of the suspensions of real toric spaces for odd primes $p$. Our decomposition is compatible with the one given by Bahri, Bendersky, Cohen, and Gitler for the suspension of the corresponding real moment-angle complex, or more generally, the polyhedral product. As an application, we obtain a stable rigidity property for real toric spaces.