$p$-local stable splitting of quasitoric manifolds

TL;DR

This paper presents a homotopy decomposition of the $p$-localized suspension of quasitoric manifolds using power maps, and explores the triviality of certain projections in this context.

Contribution

It introduces a new homotopy decomposition technique for $p$-localized suspensions of quasitoric manifolds and analyzes the triviality of associated projections.

Findings

Homotopy decomposition of ${p}$-localized suspension of quasitoric manifolds.

Triviality of the projection ${ ext{from moment-angle complex to } M}$ for $p > ext{dim } M/2$.

Discussion on the non-triviality of the projection ${ ext{and its suspension}}$.

Abstract

We show a homotopy decomposition of $p$-localized suspension $\Sigma M_{(p)}$ of a quasitoric manifold $M$ by constructing power maps. As an application we investigate the $p$-localized suspension of the projection $\pi$ from the moment-angle complex onto $M$, from which we deduce its triviality for $p>\dim M/2$. We also discuss non-triviality of $\pi_{(p)}$ and $\Sigma^\infty\pi$.