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Loose Engel structures
- Part of
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- Journal:
- Compositio Mathematica / Volume 156 / Issue 2 / February 2020
- Published online by Cambridge University Press:
- 06 January 2020, pp. 412-434
- Print publication:
- February 2020
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- Article
- Export citation
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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.
