2016/01/23 by Beben, Piotr, Grbić, Jelena
#05E40 #55M30 #55U10 #Algebraic Topology (math.AT) #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.1601.06297
Using the combinatorics of the underlying simplicial complex K, we give various upper and lower bounds for the Lusternik-Schnirelmann (LS) category of moment-angle complexes \zk. We describe families of simplicial complexes and combinatorial operations which allow for a systematic description of the LS category. In particular, we characterise the LS category of moment-angle complexes \zk over triangulated d-manifolds K for d≤ 2, as well as higher dimension spheres built up via connected sum, join, and vertex doubling operations. %This characterisation is given in terms of the combinatorics of K, the cup product length of H^*(\zk), as well as a certain Massey products. We show that the LS category closely relates to vanishing of Massey products in H^*(\zk) and through this connection we describe first structural properties of Massey products in moment-angel manifolds. Some of further applications include calculations of the LS category and the description of conditions for vanishing of Massey products for moment-angle manifolds over fullerenes, Pogorelov polytopes and k-neighbourly complexes, which double as important examples of hyperbolic manifolds.