Cup-products in generalized moment-angle complexes

Abstract

Given a family of based CW-pairs $(\underline{X},\underline{A})=\{(X;A){\}}_{i=1}^m$ together with an abstract simplicial complex $K$ with $m$ vertices, there is an associated based CW-complex $Z(K;(\underline{X},\underline{A}))$ known as a generalized moment-angle complex. The decomposition theorem of \cite{bbcg}, \cite{bbcg2} splits the suspension of $Z(K;(\underline{X},\underline{A}))$ 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; (\underline{X}, \underline{A})). Explicit computations are made for families of suspension pairs and for the cases where $X_i$ is the cone on $A_i$. 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.

An example is corrected

References in corpus (1)

• The polyhedral product functor: a method of computation for moment-angle complexes, arrangements and related spaces

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