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Momentangle complexes, monomial ideals, and Massey products
 Pure and Applied Math. Quarterly
"... Abstract. Associated to every finite simplicial complex K there is a “momentangle” finite CWcomplex, ZK; if K is a triangulation of a sphere, ZK is a smooth, compact manifold. Building on work of Buchstaber, Panov, and Baskakov, we study the cohomology ring, the homotopy groups, and the triple Mas ..."
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Cited by 44 (8 self)
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Abstract. Associated to every finite simplicial complex K there is a “momentangle” finite CWcomplex, ZK; if K is a triangulation of a sphere, ZK is a smooth, compact manifold. Building on work of Buchstaber, Panov, and Baskakov, we study the cohomology ring, the homotopy groups, and the triple Massey products of a momentangle complex, relating these topological invariants to the algebraic combinatorics of the underlying simplicial complex. Applications to the study of nonformal manifolds and subspace arrangements are given. Contents
MOMENTANGLE COMPLEXES, GOLODNESS AND SEQUENTIALLY COHENMACAULEY PROPERTY
"... Last years the construction of generalized momentangle complexes attracted a lot of interest. The connections with many other famous constructions were found, such as subspace arrangements, toric manifolds, resolutions of monomial rings etc. This leads to the important question of describing the ho ..."
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Last years the construction of generalized momentangle complexes attracted a lot of interest. The connections with many other famous constructions were found, such as subspace arrangements, toric manifolds, resolutions of monomial rings etc. This leads to the important question of describing the homotopy type of momentangle complexes, and finding their algebraic invariants.
LOOPS ON POLYHEDRAL PRODUCTS AND DIAGONAL ARRANGEMENTS
, 901
"... Abstract. This is the first of a series of papers that investigates the loop space homology of polyhedral products. To any simplicial complex K on m vertices there corresponds a polyhedral product functor, which associates to m based topological spaces X = (X1,..., Xm) a certain subspace XK in the c ..."
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Abstract. This is the first of a series of papers that investigates the loop space homology of polyhedral products. To any simplicial complex K on m vertices there corresponds a polyhedral product functor, which associates to m based topological spaces X = (X1,..., Xm) a certain subspace XK in the cartesian product ∏ i Xi. In this paper we establish a connection between the loop space homology of polyhedral products of any 1connected spaces and the homology of certain diagonal arrangements associated with K. This reduces the problem to the calculation of the Extalgebra of the exterior StanleyReisner algebra of K. We illustrate these results by finding the presentation of such loop homology algebras for flag complexes and skeletons of simplices, generalizing results of PanovRay, PapadimaSuciu, Lemaire. Finally, we show that in the case when all the Xi’s are suspensions, the homology splitting comes from the stable homotopy splitting of Ω(XK). 1.