Homological Domination in Large Random Simplicial Complexes
Abstract
In this paper we state the homological domination principle for random multi-parameter simplicial complexes, claiming that the Betti number in one specific dimension (which is explicitly determined by the probability multi-parameter) significantly dominates the Betti numbers in all other dimensions. We also state and discuss evidence for two interesting conjectures which would imply a stronger version of the homological domination principle, namely that generically homology of a random simplicial complex coincides with that of a wedges of k-dimensional spheres. These two conjectures imply that under an additional assumption (specified in the paper) a random simplicial complex collapses to a k-dimensional complex homotopy equivalent to a wedge of spheres of dimension k.
Keywords
Cite
@article{arxiv.1503.03253,
title = {Homological Domination in Large Random Simplicial Complexes},
author = {A. Costa and M. Farber},
journal= {arXiv preprint arXiv:1503.03253},
year = {2015}
}
Comments
8 pages, 1 figure