THE THRESHOLD FUNCTION FOR VANISHING OF THE TOP HOMOLOGY GROUP OF RANDOM d-COMPLEXES

For positive integers ç and d, and the probability function 0 ≤ p(n) ≤ 1, we let Y n,p,d denote the probability space of all at most d-dimensional simplicial complexes on n vertices, which contain the full (d — 1)-dimensional skeleton, and whose d-simplices appear with probability p(n). In this pape...

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Veröffentlicht in:	Proceedings of the American Mathematical Society 2010-12, Vol.138 (12), p.4517-4527
1. Verfasser:	KOZLOV, DMITRY N.
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebraic topology Coefficients Connectivity Exact sciences and technology General mathematics General, history and biography Integers Mathematical functions Mathematical theorems Mathematics Preprints Probabilities Sciences and techniques of general use Skeleton Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds Vertices
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Zusammenfassung:	For positive integers ç and d, and the probability function 0 ≤ p(n) ≤ 1, we let Y n,p,d denote the probability space of all at most d-dimensional simplicial complexes on n vertices, which contain the full (d — 1)-dimensional skeleton, and whose d-simplices appear with probability p(n). In this paper we determine the threshold function for vanishing of the top homology group in Y n,p,d, for all d ≥ 1.
ISSN:	0002-9939 1088-6826
DOI:	10.1090/S0002-9939-2010-10596-8