How many simplices are needed to triangulate a Grassmannian?

Dejan Govc; Wacław Marzantowicz; Petar Pavešić

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arXiv · 2001.08292

How many simplices are needed to triangulate a Grassmannian?

Dejan Govc·Wacław Marzantowicz·Petar Pavešić

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Abstract

We compute a lower bound for the number of simplices that are needed to triangulate the Grassmann manifold $G_k(\mathbb{R}^n)$. In particular, we show that the number of top-dimensional simplices grows exponentially with $n$. More precise estimates are given for $k=2,3,4$. Our method can be used to estimate the minimal size of triangulations for other spaces, like Lie groups, flag manifolds, Stiefel manifolds etc.

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Dejan Govc, Wacław Marzantowicz, Petar Pavešić. 2020-01-22. How many simplices are needed to triangulate a Grassmannian?. https://arxiv.org/abs/2001.08292

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