Equivariant cohomology of moment-angle complexes with respect to coordinate subtori

TL;DR

This paper calculates the equivariant cohomology of moment-angle complexes under coordinate subtorus actions, providing criteria for equivariant formality and specific results for flag complexes and graphs.

Contribution

It introduces a method to compute equivariant cohomology of moment-angle complexes and establishes criteria for their equivariant formality, with special cases for flag complexes and graphs.

Findings

Computed $H^*_{T_I}(\\mathcal Z_K)$ for moment-angle complexes

Provided a criterion for equivariant formality

Derived specific results for flag complexes and graphs

Abstract

We compute the equivariant cohomology $H^*_{T_I}(\mathcal Z_K)$ of moment-angle complexes $\mathcal Z_K$ with respect to the action of coordinate subtori $T_I \subset T^m$. We give a criterion for the equivariant formality of $\mathcal Z_K$ and obtain specifications for the cases of flag complexes and graphs.