Fundamental groups of random clique complexes

2013/12/31 by Armindo Costa, Michael Farber, Danijela Horak · 1 citation
Mathematics · #math.AT #math.CO

paper · pdf · doi:10.1112/tlms/tlv001

In this revision we strengthened Theorem 3.2 and simplified its proof. arXiv admin note: substantial text overlap with arXiv:1307.3614

arxiv created 2014/11/19 · arxiv updated 2015/06/12

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.

Citations

• Geometry and Topology of Random 2-complexes

Cited by

• Large Random Simplicial Complexes, II; the fundamental groups