Moment-angle Complexes, Monomial Ideals and Massey Products

By Graham C. Denham, Alexander I. Suciu. 2005

168 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e63b77bba462fd213f9c01d7b5a787bf46131b38

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Citations in the corpus

Real quadrics in Cn, complex manifolds and convex polytopes (2006, background): “( 3 ) In [ 14 ], a preprint which appeared on the arXiv after this work was submitted, it is proven”
The polyhedral product functor: a method of computation for moment-angle complexes, arrangements and related spaces (2007, background): “MSC: primary 13F55, 14F45, 32S22, 52C35, 55U10; secondary 16E05, 57R19 Keywords: Arrangements; Cohomology ring; Moment-angle complex; Simplicial complex; Simplicial sets; Stable splittings; Stanley–Reisner ring; Suspensions; Toric varieties * Corresponding author.”
Toric Topology (2012, unknown): “Triple Massey products in the cohomology of ZK were further studied in the work of Denham and Suciu [77].”
Cohomology computations for Artin groups, Bestvina-Brady groups, and graph products (2010, background): “ead of X). Let TS 10 denote the S-fold product of copies of S1. Deﬁne TL := [ J∈S(L) TJ. (1.5) (This is a special case of the “polyhedral product” construction discussed in the next subsection and in [2, 20].) According to [9], its universal cover Te L is a CAT(0)-cubical complex and hence, is contr”
Intersections of Quadrics, Moment-angle Manifolds and Connected Sums (2009, background): “Yet for a long time no interchange occurred between the two lines of research involving the same objects, until small connections appeared in the final version of [8] and in Denham and Suciu [15].”
Categorical aspects of toric topology (2007, background): “We believe that category theory also offers an important global viewpoint, which suggests a systematic programme for the evaluation of algebraic and geometrical invariants of XK .”