TY - JOUR
T1 - A Geometric Lower Bound Theorem
AU - Adiprasito, Karim
AU - Nevo, Eran
AU - Samper, José Alejandro
N1 - Publisher Copyright:
© 2016, Springer International Publishing.
PY - 2016/4/1
Y1 - 2016/4/1
N2 - 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 C2-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.
AB - 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 C2-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.
UR - http://www.scopus.com/inward/record.url?scp=84964523466&partnerID=8YFLogxK
U2 - 10.1007/s00039-016-0363-x
DO - 10.1007/s00039-016-0363-x
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AN - SCOPUS:84964523466
SN - 1016-443X
VL - 26
SP - 359
EP - 378
JO - Geometric and Functional Analysis
JF - Geometric and Functional Analysis
IS - 2
ER -