A Geometric Lower Bound Theorem
Metric Geometry
2016-02-18 v4 Combinatorics
Abstract
We resolve a conjecture of Kalai relating approximation theory of convex bodies by simplicial polytopes to the face numbers and primitive Betti numbers of these polytopes and their toric varieties. The proof uses higher notions of chordality. Further, for C^2-convex bodies, asymptotically tight lower bounds on the g-numbers of the approximating polytopes are given, in terms of their Hausdorff distance from the convex body.
Keywords
Cite
@article{arxiv.1507.06638,
title = {A Geometric Lower Bound Theorem},
author = {Karim Adiprasito and Eran Nevo and José Alejandro Samper},
journal= {arXiv preprint arXiv:1507.06638},
year = {2016}
}
Comments
26 pages, 6 figures, to appear in Geometric and Functional Analysis