Cup-products in generalized moment-angle complexes

الأصل · EN

Given a family of based CW-pairs (X,A)={(X;A)}ᵐᵢ₌₁ together with an abstract simplicial complex K with m vertices, there is an associated based CW-complex Z(K;(X,A)) known as a generalized moment-angle complex. The decomposition theorem of bbcg, bbcg2 splits the suspension of Z(K; (X, A)) into a bouquet of spaces determined by the full sub-complexes of K. Thatdecomposition theorem is used here to describe the ring structure for the cohomology of Z(K; (X, A)). Explicit computations are made for families of suspension pairs and for the cases where Xᵢ is the cone on Aᵢ. These results complement and generalize those of Davis-Januszkiewicz, Franz, Hochster as well as Panov, and Baskakov-Buchstaber-Panov. Under conditions stated below, these theorems also apply for generalized cohomology theories.