Moment-angle manifolds corresponding to three-dimensional simplicial spheres, chordality and connected sums of products of spheres

2024/08/09 by Oganisian, Victoria, Panov, Taras
#57N65 #57S12 #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2408.04843

Abstract

We prove that the moment-angle complex \mathcal Z_K corresponding to a 3-dimensional simplicial sphere K has the cohomology ring isomorphic to the cohomology ring of a connected sum of products of spheres if and only if either (a) K is the boundary of a 4-dimensional cross-polytope, or (b) the one-skeleton of K is a chordal graph, or (c) there are only two missing edges in K and they form a chordless 4-cycle. For simplicial spheres K of arbitrary dimension, we obtain a sufficient condition for the ring isomorphism H^*(\mathcal Z_K)≅ H^*(M) where M is a connected sum of products of spheres.

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