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Keywords:

  • homology;
  • random simplicial complex

Abstract

Let Δn−1 denote the (n − 1)-dimensional simplex. Let Y be a random k-dimensional subcomplex of Δn−1 obtained by starting with the full (k − 1)-dimensional skeleton of Δn−1 and then adding each k-simplex independently with probability p. Let Hk−1(Y; R) denote the (k − 1)-dimensional reduced homology group of Y with coefficients in a finite abelian group R. It is shown that for any fixed R and k ≥ 1 and for any function ω(n) that tends to infinity

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© 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2009