On the genus of real projective spaces

Abstract.

We construct a crystallization of the real projective space ${\mathbb{R}}P^n$ whose associated contracted complex is minimal with respect to the number of n-simplexes. Then we compute the regular genus of ${\mathbb{R}}P^n$, which is the minimum genus of a closed connected surface into which a crystallization of ${\mathbb{R}}P^n$ regularly embeds.