ИСТИНА

We put a cochain complex structure CH*(Z_K) on the cohomology of a moment-angle complex Z_K by defining a new differential d' on the Hochster decomposition of the Tor-algebra of the face ring of a simplicial complex K. We call the cohomology of CH*(Z_K) the double cohomology, HH*(Z_K). It can be identified with the second double cohomology of a bicomplex obtained by adding the second differential d' to the Koszul differential graded algebra of the face ring of K. We analyse HH*(Z_K) and compute it for several families of K, including flag complexes with chordal 1-skeleta. Our motivation for defining HH*(Z_K) comes from persistent cohomology. The double cohomology possesses a stability property, unlike the ordinary cohomology H*(Z_K).