The homotopical dimension of random 2-complexes

Mathematics – Algebraic Topology

Scientific paper

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Scientific paper

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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