A new family of triangulations of $\mathbb{R}{P}^d$

Abstract

We construct a family of PL triangulations of the $d$-dimensional real projective space $\mathbb{R}{P}^d$ on $\Theta ((\frac{1+\sqrt{5}}{2}{)}^{d+1})$ vertices for every $d\ge 1$. This improves a construction due to Kühnel on $2^{d+1}-1$ vertices.

13 pages, 3 figures. Minor revision