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Article

Approximate Triangulations of Grassmann Manifolds

Department of Mathematics, University of Florida, Gainesville, FL 32611, USA
Algorithms 2020, 13(7), 172; https://doi.org/10.3390/a13070172
Received: 24 June 2020 / Revised: 14 July 2020 / Accepted: 16 July 2020 / Published: 17 July 2020
(This article belongs to the Special Issue Topological Data Analysis)
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 ) . View Full-Text
Keywords: Grassmannian; persistent homology; Vietoris–Rips complex; witness complex; triangulation Grassmannian; persistent homology; Vietoris–Rips complex; witness complex; triangulation
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MDPI and ACS Style

Knudson, K.P. Approximate Triangulations of Grassmann Manifolds. Algorithms 2020, 13, 172. https://doi.org/10.3390/a13070172

AMA Style

Knudson KP. Approximate Triangulations of Grassmann Manifolds. Algorithms. 2020; 13(7):172. https://doi.org/10.3390/a13070172

Chicago/Turabian Style

Knudson, Kevin P. 2020. "Approximate Triangulations of Grassmann Manifolds" Algorithms 13, no. 7: 172. https://doi.org/10.3390/a13070172

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