Compression bounds for Lipschitz maps from the Heisenberg group to $L_1$
Metric Geometry
2009-10-13 v1 Data Structures and Algorithms
Differential Geometry
Functional Analysis
Group Theory
Abstract
We prove a quantitative bi-Lipschitz nonembedding theorem for the Heisenberg group with its Carnot-Carath\'eodory metric and apply it to give a lower bound on the integrality gap of the Goemans-Linial semidefinite relaxation of the Sparsest Cut problem.
Keywords
Cite
@article{arxiv.0910.2026,
title = {Compression bounds for Lipschitz maps from the Heisenberg group to $L_1$},
author = {Jeff Cheeger and Bruce Kleiner and Assaf Naor},
journal= {arXiv preprint arXiv:0910.2026},
year = {2009}
}