The homotopical dimension of random 2-complexes

Published 19 May 2010 in math.AT and math.PR | (1005.3383v1)

Abstract: In this paper we study the Linial-Meshulam model of random two-dimensional complexes. We prove that a random 2-complex is homotopically one dimensional, with probability tending to one as n tends to infitnity, assuming that the probability parameter p satisfies pn --> 0.

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