Double cohomology of moment-angle complexes

Abstract

We put a cochain complex structure ${CH}^{\ast }({\mathcal{Z}}_K)$ on the cohomology of a moment-angle complex ${\mathcal{Z}}_K$ and call the resulting cohomology the double cohomology, ${HH}^{\ast }({\mathcal{Z}}_K)$. We give three equivalent definitions for the differential, and compute ${HH}^{\ast }({\mathcal{Z}}_K)$ for a family of simplicial complexes containing clique complexes of chordal graphs.

25 pages, 4 figures, published version