Geometry and Topology of Random 2-complexes

Abstract

We study random 2-dimensional complexes in the Linial - Meshulam model and find torsion in their fundamental groups at various regimes. We find a simple algorithmically testable criterion for a subcomplex of a random 2-complex to be aspherical; this implies that any aspherical subcomplex of a random 2-complex satisfies the Whitehead conjecture. We use inequalities for Cheeger constants and systoles of simplicial surfaces to analyse spheres and projective planes lying in random 2-complexes. Our proofs exploit the strong hyperbolicity property of random 2-complexes.

37 pages

References in corpus (1)

• Collapsibility and vanishing of top homology in random simplicial complexes

Cited by in corpus (3)

• Fundamental groups of random clique complexes
• Homological Domination in Large Random Simplicial Complexes
• Large random simplicial complexes, I