Polyhedral products associated to pseudomanifolds

TL;DR

This paper explores the homotopy theory of polyhedral products linked to pseudomanifolds, revealing decompositions of loop spaces of certain moment-angle manifolds into products of spheres and loops on spheres.

Contribution

It introduces a homotopy-theoretic framework for polyhedral products related to pseudomanifolds and demonstrates explicit decompositions for specific cases.

Findings

Loop spaces of moment-angle manifolds decompose into products of spheres.

Polyhedral products associated to pseudomanifolds have tractable homotopy types.

Decomposition results apply to triangulations of S^2 and S^3.

Abstract

We study the homotopy theory of polyhedral products associated to a combinatorial generalisation of manifolds known as pseudomanifolds. As special cases, we show that loop spaces of moment-angle manifolds associated to triangulations of $S^2$ and $S^3$ decompose as a product of spheres and loops on spheres.