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 \( H_{1} {\left( {Y;{\Bbb F}_{2} } \right)} \) denote the first homology group of Y with mod 2 coefficients. It is shown that for any function ω(n) that tends to infinity

Authors and Affiliations

1. Department of Computer Science, Hebrew University, Jerusalem 91904, Israel

   Nathan Linial*

2. Department of Mathematics, Technion, Haifa 32000, Israel

   Roy Meshulam*

Corresponding author

Correspondence to Nathan Linial*.

* Supported by an Israel Science Foundation grant.

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