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Moment angle complexes, monomial ideals, and Massey products

Domenii publicaţii > Matematica + Tipuri publicaţii > Articol în revistã ştiinţificã

Autori: G. Denham, A. I. Suciu

Editorial: Pure and Applied Mathematics Quarterly, 3 (1), p.25-60, 2007.


Associated to every finite simplicial complex K there is a „moment-angle” finite CW-complex, Z_K; if K is a triangulation of a sphere, Z_K 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 moment-angle complex, relating these topological invariants to the algebraic combinatorics of the underlying simplicial complex. Applications to the study of non-formal manifolds and subspace arrangements are given.

Cuvinte cheie: Moment-angle complex, cohomology ring, homotopy Lie algebra, Stanley-Reisner ring, Eilenberg-Moore spectral sequence, cellular cochain algebra, formality, Massey product, triangulation, Bier sphere, subspace arrangement, complex manifold