Approximate Triangulations of Grassmann Manifolds

Abstract

We define the notion of an approximate triangulation for a manifold M embedded in Euclidean space. The basic idea is to build a nested family of simplicial complexes whose vertices lie in M and use persistent homology to find a complex in the family whose homology agrees with that of M. Our key examples are various Grassmann manifolds G k ( R n ) .

Keywords

• Grassmannian
• persistent homology
• Vietoris–Rips complex
• witness complex
• triangulation