English

On the extension of bi-Lipschitz mappings

Geometric Topology 2020-01-06 v1

Abstract

Let XX be a closed semialgebraic set of dimension k.k. If n2k+1n\ge 2k+1, then there is a bi-Lipschitz and semialgebraic embedding of XX into Rn.\Bbb R^n. Moreover, if n2k+2n \ge 2k+2, then this embedding is unique (up to a bi-Lipschitz and semialgebraic homeomorphism of Rn.\Bbb R^n.

Keywords

Cite

@article{arxiv.2001.00753,
  title  = {On the extension of bi-Lipschitz mappings},
  author = {Lev Birbrair and Alexandre Fernandes and Zbigniew Jelonek},
  journal= {arXiv preprint arXiv:2001.00753},
  year   = {2020}
}