Compression bounds for Lipschitz maps from the Heisenberg group to L1

@article{Cheeger2009CompressionBF,
  title={Compression bounds for Lipschitz maps from the Heisenberg group to L1},
  author={Jeff Cheeger and Bruce Kleiner and Assaf Naor},
  journal={CoRR},
  year={2009},
  volume={abs/0910.2026}
}
We prove a quantitative bi-Lipschitz nonembedding theorem for the Heisenberg group with its Carnot-Carathéodory metric and apply it to give a lower bound on the integrality gap of the Goemans-Linial semidefinite relaxation of the Sparsest Cut problem. 
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