{
  "id": "math/0005199",
  "version": "v1",
  "published": "2000-05-20T12:54:46.000Z",
  "updated": "2000-05-20T12:54:46.000Z",
  "title": "Moment-angle complexes and combinatorics of simplicial manifolds",
  "authors": [
    "Victor M. Buchstaber",
    "Taras E. Panov"
  ],
  "comment": "28 pages, LaTeX2e, extended version of the paper published in Russian Math. Surveys 55 (2000), no. 3",
  "categories": [
    "math.AT",
    "math.CO",
    "math.DG"
  ],
  "abstract": "Let $\\rho:(D^2)^m\\to I^m$ 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 $\\rho^{-1}(C)\\subset(D^2)^m$ 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-05-20T12:54:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B70",
      "57R19",
      "57Q15"
    ],
    "keywords": [
      "simplicial manifold",
      "combinatorics",
      "corresponding moment-angle complexes",
      "simplicial complexes",
      "invariant bigraded cellular decomposition"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 28,
      "language": "ru",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......5199B"
    }
  }
}