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

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.