Cup-products in generalized moment-angle complexes

2010/01/19 by Bahri, A., Bendersky, M., Cohen, F. R. +1
#Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1001.3372

Abstract

Given a family of based CW-pairs (\underlineX,\underlineA)=\(X;A)\^m_i=1 together with an abstract simplicial complex K with m vertices, there is an associated based CW-complex Z(K;(\underlineX,\underlineA)) known as a generalized moment-angle complex. The decomposition theorem of \citebbcg, \citebbcg2 splits the suspension of Z(K; (\underlineX, \underlineA)) 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; (\underlineX, \underlineA)). 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.

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