Toral rank conjecture for moment-angle complexes.

link: http://arxiv.org/abs/0909.1053
Abstract

In this paper we consider an operation on the set of simplicial complexes,
which we call "doubling operation". We show that the moment-angle complex Z_K
is the real moment-angle complex RZ_L(K) for simplicial complex L(K) obtained
from K by applying "doubling operation". As an application of this operation we
prove the toral rank conjecture for Z_K by estimating the lower bound of the
cohomology rank (with rational coefficients) of the real moment-angle complexes
RZ_K.