Loose Engel structures

A. del Pino Gomez, Roger Casals, Francisco Presas

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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.
Original languageUndefined/Unknown
Number of pages23
JournalCompositio Mathematica
Issue number2
Publication statusPublished - Feb 2020


  • Engel structures
  • h-principle
  • flexibility

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