Arya Narnapatti

Superpolynomial lower bounds for vertex numbers of real projective space triangulations via a topological Figiel-Lindenstrauss-Milman theorem

We prove that every simplicial triangulation of real projective $d$-space has $\exp(\Omega(\sqrt d))$ vertices. Together with known constructions, this determines the minimum vertex number as $\mu_d=\exp(d^{1/2+o(1)})$. The result follows from a topological generalization of the Figiel--Lindenstrauss--Milman inequality...