Compositio Mathematica ( IF 1.200 ) Pub Date : 2020-01-06 , DOI: 10.1112/s0010437x19007759
Roger Casals; Álvaro del Pino; Francisco Presas

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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