Moment-angle manifolds associated to neighbourly triangulations of spheres

TL;DR

This paper proves that moment-angle manifolds derived from neighborly sphere triangulations are homotopy equivalent to connected sums of sphere products, solving a longstanding problem.

Contribution

It introduces a homotopy theoretic approach to characterize moment-angle manifolds for neighborly sphere triangulations, extending to generalized cases.

Findings

Homotopy equivalence to connected sums of sphere products

Resolution of a problem posed by Buchstaber and Panov

Extension to generalized moment-angle manifolds

Abstract

We show that a moment-angle manifold associated to a neighbourly triangulation of an odd dimensional sphere is homotopy equivalent to a connected sum of products of two spheres, resolving a problem of Buchstaber and Panov. The methods are entirely homotopy theoretic, allowing for an extension to a corresponding result in the case of generalized moment-angle manifolds.