Doubling operation for polytopes and torus actions

TL;DR

This paper introduces a doubling operation for simple polytopes, derives formulas for their h-polynomials, and applies this to relate moment-angle manifolds and their real versions, proving the toral rank conjecture.

Contribution

It defines the doubling operation for polytopes, provides formulas for the h-polynomial of the resulting polytope, and proves the toral rank conjecture for moment-angle manifolds.

Findings

Derived the formula for the h-polynomial of doubled polytopes

Established the relationship between moment-angle manifolds and their real analogues

Proved the toral rank conjecture for moment-angle manifolds Z_P

Abstract

In this note we give the definition of the "doubling operation" for simple polytopes, find the formula for the h-polynomial of new polytope.As an application of this operation we establish the relationship between moment-angle manifolds and their real analogues and prove the toral rank conjecture for moment-angle manifolds Z_P.