Approximate Triangulations of Grassmann Manifolds

Approximate Triangulations of Grassmann Manifolds

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 exam...

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Veröffentlicht in:Algorithms 2020-07, Vol.13 (7), p.172
1. Verfasser: Knudson, Kevin P.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Apexes
Decomposition
Euclidean geometry
Euclidean space
Grassmannian
Homology
Manifolds (mathematics)
persistent homology
Triangulation
Vietoris–Rips complex
witness complex
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Zusammenfassung: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 ) .
ISSN:1999-4893
1999-4893
DOI:10.3390/a13070172