The G-index, G-coindex and G-weight of a real moment-angle complex

TL;DR

This paper introduces combinatorial invariants called G-index, G-coindex, and G-weight for real moment-angle complexes, which are CW complexes associated with simplicial complexes and equipped with a 2-torus action.

Contribution

It provides a combinatorial description of these invariants for subtorus actions on real moment-angle complexes, advancing understanding of their symmetry properties.

Findings

Defined G-index, G-coindex, and G-weight invariants.

Provided combinatorial formulas for these invariants.

Enhanced understanding of torus actions on moment-angle complexes.

Abstract

A real moment-angle complex is a CW complex defined by the combinatoric information of a simplicial complex, and has a standard action of $2$-torus. For each subtorus $G$ of $2$-torus, we describe invariants corcerning this action, the $G$-index, $G$-coindex and $G$-weight, combinatorially.