A subexponential size triangulation of ${\mathbb R}P^n$

Abstract: A practical way to encode a manifold is to triangulate it. Among all possible triangulations it makes sense to look for the minimal one, which for the purpose of this talk means using the least number of vertices.

Consider a family of manifolds such as $S^n$, ${\mathbb R}P^n$, $SO_n$, etc. A natural question is how the size of the minimal triangulation depends on $n$? Surprisingly, except for the trivial case of $S^n$, our best lower and upper bounds are very far apart.

For ${\mathbb R}P^n$ the current best lower and upper bounds are around $n^2$ and $\phi^n$, respectively, where $\phi$ is the golden ratio. In this talk I will present the first triangulation of ${\mathbb R}P^n$ with a subexponential, approximately $\sqrt{n}^\sqrt{n}$, number of vertices. I will also state several open problems related to the topic.

This is a joint work with Karim Adiprasito and Roman Karasev.

computational geometrydiscrete mathematicsdata structures and algorithmscombinatorics

Audience: researchers in the discipline

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Discrete and Computational Geometry Seminar in Paris

Series comments: Language is English if anyone in the audience prefers it (otherwise French).

Links and passwords for the talks are on the seminar homepage: monge.univ-mlv.fr/~hubard/GAC/

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