Loose Engel structures

  title={Loose Engel structures},
  author={Roger Casals and {\'A}lvaro del Pino and F. Presas},
  journal={Compositio Mathematica},
  pages={412 - 434}
This paper contributes to the study of Engel structures and their classification. The main result introduces the notion of a loose family of Engel structures and shows that two such families are Engel homotopic if and only if they are formally homotopic. This implies a complete $h$-principle when auxiliary data is fixed. As a corollary, we show that Lorentz and orientable Cartan prolongations are classified up to homotopy by their formal data. 
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