Sharp vanishing thresholds for cohomology of random flag complexes
Type:
Papers
Publisher:
Annals of Mathematics
Submitted:
Jul 2012
Accepted:
Sep 2013
Publication date:
2014
Abstract:
We exhibit a sharp threshold for vanishing of rational cohomology in random flag complexes, providing a generalization of the Erdős–Rényi theorem. As a corollary, almost all $d$-dimensional flag complexes have nontrivial (rational, reduced) homology only in middle degree $\lfloor d/2 \rfloor$.
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