Homological connectivity of random k‐dimensional complexes

Abstract

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