Higher dimensional distortion of random complexes
Metric Geometry
2014-10-29 v3 Combinatorics
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.
Cite
@article{arxiv.1210.6951,
title = {Higher dimensional distortion of random complexes},
author = {Dominic Dotterrer},
journal= {arXiv preprint arXiv:1210.6951},
year = {2014}
}
Comments
15 pages, additional comments on the work of Newman and Rabinovich added