Geometry and Topology of Random 2-complexes

A. E. Costa; M. Farber

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arXiv · 1307.3614

Geometry and Topology of Random 2-complexes

A. E. Costa·M. Farber

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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.

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BibTeX RIS

A. E. Costa, M. Farber. 2013-07-13. Geometry and Topology of Random 2-complexes. https://arxiv.org/abs/1307.3614

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