Triangulations of ${\mathbb{RP}}^n$ with few vertices

Abstract

P. Arnoux and A. Marin showed that any triangulation of ${\mathbb{RP}}^n$ contains more than $\frac{(n+1)(n+2)}{2}$ vertices if $n\ge 3$. We construct some natural triangulation of ${\mathbb{RP}}^n$ with $\frac{n(n+5)}{2}-1$ vertices for all $n\ge 3$. Previously, it was known that ${\mathbb{RP}}^n$ has ${\mathbb{Z}}_2^n$-equivariant triangulation with $n(n+1)$ vertices for $n\ge 6$.

There is a logical gap in the proof of the main theorem

References in corpus (1)

• Triangulated Manifolds with Few Vertices: Combinatorial Manifolds