Sampling $C^1$-submanifolds of $\mathbb{H}^n$

DOI10.4064/cm8447-6-2021zbMath1492.53012OpenAlexW4206032252MaRDI QIDQ5074199

Aleksander Antasik

Publication date: 9 May 2022

Published in: Colloquium Mathematicum (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4064/cm8447-6-2021

zbMATH Keywords

homotopy typesubmanifoldhyperbolic spacehomotopy equivalencemanifold learningreach

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Homotopy equivalences in algebraic topology (55P10) Non-Euclidean differential geometry (53A35) Applications of differential geometry to data and computer science (53Z50)

Uses Software

• GeoGebra

Cites Work

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• Sets with positive reach
• Only distances are required to reconstruct submanifolds
• Nerves, fibers and homotopy groups
• Vietoris-Rips complexes also provide topologically correct reconstructions of sampled shapes
• Cone fields and topological sampling in manifolds with bounded curvature
• Finding the homology of submanifolds with high confidence from random samples
• Curvature Measures
• Geometric and Topological Inference
• Nonlinear Dimensionality Reduction
• On the imbedding of systems of compacta in simplicial complexes

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