On the extension of bi-Lipschitz mappings

• Lev Birbrair ^[1] ; Alexandre Fernandes ^[1] ; Zbigniew Jelonek ^[2]
  1. [1] Universidade Federal do Ceará

     Universidade Federal do Ceará

     Brasil

     
  2. [2] Polska Akademia Nauk, Polonia
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 27, Nº. 2, 2021
• Idioma: inglés
• DOI: 10.1007/s00029-021-00625-6
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• Resumen

  • Let X be a closed semialgebraic set of dimension k. If n≥2k+1, then there is a bi-Lipschitz and semialgebraic embedding of X into Rn. Moreover, if n≥2k+2, then this embedding is unique (up to a bi-Lipschitz and semialgebraic homeomorphism of Rn). We also give local and complex algebraic counterparts of these results.