Moment-angle complexes and combinatorics of simplicial manifolds

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dc.creatorBuchstaber, Victor M.
dc.creatorPanov, Taras E.
dc.date2000-05-20
dc.date.accessioned2026-07-07T04:35:24Z
dc.date.available2026-07-07T04:35:24Z
dc.descriptionLet $ρ:(D^2)^m\to I^m$ be the orbit map for the diagonal action of the torus $T^m$ on the unit poly-disk $(D^2)^m$, $I^m=[0,1]^m$ is the unit cube. Let $C$ be a cubical subcomplex in $I^m$. The moment-angle complex $\ma(C)$ is a $T^m$-invariant bigraded cellular decomposition of the subset $ρ^{-1}(C)\subset(D^2)^m$ with cells corresponding to the faces of $C$. Different combinatorial problems concerning cubical complexes and related combinatorial objects can be treated by studying the equivariant topology of corresponding moment-angle complexes. Here we consider moment-angle complexes defined by canonical cubical subdivisions of simplicial complexes. We describe relations between the combinatorics of simplicial complexes and the bigraded cohomology of corresponding moment-angle complexes. In the case when the simplicial complex is a simplicial manifold the corresponding moment-angle complex has an orbit consisting of singular points. The complement of an invariant neighbourhood of this orbit is a manifold with boundary. The relative Poincare duality for this manifold implies the generalized Dehn-Sommerville equations for the number of faces of simplicial manifolds.
dc.description28 pages, LaTeX2e, extended version of the paper published in Russian Math. Surveys 55 (2000), no. 3
dc.identifierhttps://arxiv.org/abs/math/0005199
dc.identifierhttp://arxiv.org/abs/math/0005199
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59239
dc.subjectAlgebraic Topology
dc.subjectCombinatorics
dc.subjectDifferential Geometry
dc.subject52B70; 57R19; 57Q15
dc.titleMoment-angle complexes and combinatorics of simplicial manifolds
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