Homological Connectivity Of Random 2-Complexes

Let Δ_n−1 denote the (n − 1)-dimensional simplex. Let Y be a random 2-dimensional subcomplex of Δ_n−1 obtained by starting with the full 1-dimensional skeleton of Δ_n−1 and then adding each 2−simplex independently with probability p. Let denote the first homology group of Y with mod 2 coefficients. It is shown that for any function ω(n) that tends to infinity * Supported by an Israel Science Foundation grant.