English

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.

Keywords

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

R2 v1 2026-06-22T02:20:44.724Z