Higher dimensional distortion of random complexes
Dominic Dotterrer · Mathematical Research Letters · 2015
Using the random complexes of Linial and Meshulam [17], 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.