On a vertex-minimal triangulation of \(\mathbb R \mathrm P^4\)

Sonia Balagopalan¹

¹Department of Mathematics and Statistics, Maynooth University

The electronic journal of combinatorics, Tome 24 (2017) no. 1

Résumé

We give three constructions of a vertex-minimal triangulation of $4$-dimensional real projective space $\mathbb{R}\mathrm{P}^4$. The first construction describes a $4$-dimensional sphere on $32$ vertices, which is a double cover of a triangulated $\mathbb{R}\mathrm{P}^4$ and has a large amount of symmetry. The second and third constructions illustrate approaches to improving the known number of vertices needed to triangulate $n$-dimensional real projective space. All three constructions deliver the same combinatorial manifold, which is also the same as the only known $16$-vertex triangulation of $\mathbb{R}\mathrm{P}^4$. We also give a short, simple construction of the $22$-point Witt design, which is closely related to the complex we construct.

Détail

DOI : 10.37236/5956

Classification : 05E45, 05E30, 52B70
Mots-clés : combinatorial manifolds, vertex-minimal, minimal triangulation, projective space, Witt design