Higher dimensional distortion of random complexes

Using the random complexes of Linial and Meshulam [N. Linial and R. Meshulam, “Homological connectivity of random 2-complexes” Combinatorica, 26 (2006), pp. 475–487], 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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Published 13 April 2016