Fundamental groups of random clique complexes
Algebraic Topology
2015-06-12 v3 Combinatorics
Abstract
We study fundamental groups of clique complexes associated to random graphs. We establish thresholds for their cohomological and geometric dimension and torsion. We also show that in certain regime any aspherical subcomplex of a random clique complex satisfies the Whitehead conjecture, i.e. all irs subcomplexes are also aspherical.
Cite
@article{arxiv.1312.1208,
title = {Fundamental groups of random clique complexes},
author = {Armindo Costa and Michael Farber and Danijela Horak},
journal= {arXiv preprint arXiv:1312.1208},
year = {2015}
}
Comments
In this revision we strengthened Theorem 3.2 and simplified its proof. arXiv admin note: substantial text overlap with arXiv:1307.3614