Fundamental groups of random clique complexes

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.

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

References in corpus (3)

• Freiheitssatz and phase transition for the density model of random groups
• Fundamental Groups of Random Clique Complexes
• The asphericity of random 2-dimensional complexes

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