ИСТИНА

In this talk we consider the ring of equivariant cohomology $H^*_{S^1_i}(Z_K)$, where $S^1_i$ is the $i$th coordinate circle in $m$--dimensional torus ${T}^m$. It is known how to calculate the ring $H^*_{S^1_i}(Z_K)$. We consider the following question: what are the necessary and sufficient conditions under which the equivariant cohomology ring $H^*_{S^1_i}(Z_K)$ is a free module over $\mathbb{Z}[\upsilon_i]$ for $\forall \, i$. The criterion for flag and one-dimensional complexes will be given in this talk.