Generalizations of the Kolmogorov–Barzdin embedding estimates
By Misha Gromov, Larry Guth. 2011
57 citations recorded by the source corpus.
We consider several ways to measure the `geometric complexity' of an embedding from a simplicial complex into Euclidean space. One of these is a version of `thickness', based on a paper of Kolmogorov and Barzdin. We prove inequalities relating the thickness and the number of simplices in the simplicial complex, generalizing an estimate that Kolmogorov and Barzdin proved for graphs. We also consider the distortion of knots. We give an alternate proof of a theorem of Pardon that there are isotopy classes of knots requiring arbitrarily large distortion. This proof is based on the expander-like properties of arithmetic hyperbolic manifolds.
Subfields: Computational Theory and Mathematics, Computer Graphics and Computer-Aided Design, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/ff863adf0c11b8869a9d49feb3a144fef14739d0
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In Computational Theory and Mathematics
In Computer Graphics and Computer-Aided Design
In Geometry and Topology
Citations in the corpus
- Expander graphs in pure and applied mathematics (2011, background): “arious networks in R3 and this way to graphs in which any two subsets have a large number of edges between them, a property which characterizes expanders (see [HLW, x2.4], and the historical notes in [GrGu]). When kis xed, bounding "- the expansion constant is closely related to the isoperimetr”