
TL;DR
This paper generalizes the Kolmogorov-Barzdin theorem for simplicial complex maps into Euclidean space, introducing sparse maps and exploring complexes with controlled 1-waist.
Contribution
It presents a new generalization of a classical theorem and introduces the concepts of sparse maps and controlled 1-waist in simplicial complexes.
Findings
Generalized Kolmogorov-Barzdin theorem for simplicial complexes
Introduction of sparse maps concept
Discussion of complexes with controlled 1-waist
Abstract
We prove a generalization of the Kolmogorov-Barzdin theorem for maps from simplicial complexes into Euclidean space. Along the way we introduce the notion of sparse maps and discuss maps from simplicial complexes with controlled 1-waist.
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Taxonomy
TopicsGeographic Information Systems Studies · Image Retrieval and Classification Techniques · Data Visualization and Analytics
