Mathematics – Algebraic Topology
Scientific paper
2010-01-19
Mathematics
Algebraic Topology
An example is corrected
Scientific paper
Given a family of based CW-pairs $(\underline{X},\underline{A})=\{(X;A)\}^m_{i=1}$ 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.
Bahri Anthony
Bendersky Martin
Cohen Frederick R.
Gitler Samuel
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