On the rank of the double cohomology of moment-angle complexes

2024/04/10 by Zhang, Zhilei
#13F55 #55N10 #55U10 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2404.06763

Abstract

In [6], the authors construct a cochain complex C H^*(Z_K) on the cohomology of a moment-angle complex Z_K and call the resulting cohomology the double cohomology, H H^*(Z_K). In this paper, we study the change of rank in double cohomology after gluing an n-simplex to a simplicial complex K in certain conditions. As an application, we give a positive answer to an open problem in [6]: For any even integer r, there always exists a simlicial complex K such that rank H H^*(Z_K)=r.

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