Higher dimensional distortion of random complexes

2012/10/25 by Dominic Dotterrer, Dotterrer, Dominic
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG) #math.CO #math.MG

paper · pdf · doi:10.48550/arxiv.1210.6951

15 pages, additional comments on the work of Newman and Rabinovich added

arxiv created 2014/10/28 · arxiv updated 2014/10/29

Abstract

Using the random complexes of Linial and Meshulam, we exhibit a large family of simplicial complexes for which, whenever affinely embedded into Euclidean space, the filling areas of simplicial cycles is greatly distorted. This phenomenon can be regarded as a higher order analogue of the metric distortion of embeddings of random graphs.

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