Moment-angle manifolds and Panov's problem

TL;DR

This paper establishes a connection between the homotopy decomposition of moment-angle complexes and the diffeomorphism decomposition of moment-angle manifolds, bridging two different approaches in the study of these geometric objects.

Contribution

It solves Panov's problem by describing the relationship between homotopy and diffeomorphism decompositions of moment-angle manifolds.

Findings

Identifies the correspondence between wedge summands and connected sum factors.

Provides a unified understanding of different decompositions of moment-angle manifolds.

Bridges homotopy and differential topology perspectives in the study of moment-angle complexes.

Abstract

We answer a problem posed by Panov, which is to describe the relationship between the wedge summands in a homotopy decomposition of the moment-angle complex corresponding to a disjoint union of k points and the connected sum factors in a diffeomorphism decomposition of the moment-angle manifold corresponding to the simple polytope obtained by making k vertex cuts on a standard d-simplex. This establishes a bridge between two very different approaches to moment-angle manifolds.