Homological connectivity of random k‐dimensional complexes |
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Authors: | R Meshulam N Wallach |
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Institution: | 1. Institute for Advanced Study, Princeton, New Jersey 08540;2. Department of Mathematics, Technion, Haifa 32000, Israel |
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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 © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2009 |
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Keywords: | homology random simplicial complex |
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