Loop space decompositions of moment-angle complexes associated to two dimensional simplicial complexes

TL;DR

This paper demonstrates that the loop space of certain moment-angle complexes derived from 2-dimensional simplicial complexes can be decomposed into a finite product of spheres, loops on spheres, and indecomposable spaces, especially after localization.

Contribution

It provides a new decomposition framework for the loop spaces of moment-angle complexes associated with 2D simplicial complexes, including conditions for prime localization.

Findings

Loop space decomposes into spheres and loops on spheres

Decomposition holds after localization away from many primes

Identifies conditions for indecomposable spaces in the decomposition

Abstract

We show that the loop space of a moment-angle complex associated to a $2$-dimensional simplicial complex decomposes as a finite type product of spheres, loops on spheres, and certain indecomposable spaces which appear in the loop space decomposition of Moore spaces. We also give conditions on certain subcomplexes under which, localised away from sufficiently many primes, the loop space of a moment-angle complex decomposes as a finite type product of spheres and loops on spheres.