Authors: Limonchenko, Ivan 
Title: Topology of moment-angle manifolds arising from flag nestohedra
Journal: Chinese Annals of Mathematics. Series B
Volume: 38
First page: 1287
Last page: 1302
Issue Date: 2017
Rank: M22
ISSN: 0252-9599
DOI: 10.1007/s11401-017-1037-1
Abstract: 
The author constructs a family of manifolds, one for each n ≥ 2, having a nontrivial Massey n-product in their cohomology for any given n. These manifolds turn out to be smooth closed 2-connected manifolds with a compact torus Tm-action called moment-angle manifolds ZP, whose orbit spaces are simple n-dimensional polytopes P obtained from an n-cube by a sequence of truncations of faces of codimension 2 only (2-truncated cubes). Moreover, the polytopes P are flag nestohedra but not graph-associahedra. The author also describes the numbers β−i,2(i+1)(Q) for an associahedron Q in terms of its graph structure and relates it to the structure of the loop homology (Pontryagin algebra) H*(ΩZQ), and then studies higher Massey products in H*(ZQ) for a graph-associahedron Q.
Keywords: Flag nestohedra | Graph-associahedron | Massey products | Moment-angle manifold | Stanley-Reisner ring
Publisher: Springer Link

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