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Loose Engel structures

Part of: General theory of differentiable manifolds

Published online by Cambridge University Press:  06 January 2020

Roger Casals ,
Álvaro del Pino  and
Francisco Presas
Roger Casals
Affiliation:
University of California Davis, Department of Mathematics, Shields Avenue, Davis, CA 95616, USA email casals@math.ucdavis.edu
Álvaro del Pino
Affiliation:
Utrecht University, Department of Mathematics, Budapestlaan 6, 3584 CD Utrecht, The Netherlands email a.delpinogomez@uu.nl
Francisco Presas
Affiliation:
Instituto de Ciencias Matemáticas – CSIC, C. Nicolás Cabrera 13–15, 28049 Madrid, Spain email fpresas@icmat.es
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Abstract

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.

Keywords

Engel structuresh-principleflexibility

MSC classification

Primary: 58A17: Pfaffian systems 58A30: Vector distributions (subbundles of the tangent bundles)
Type
Research Article
Information
Compositio Mathematica , Volume 156 , Issue 2 , February 2020 , pp. 412 - 434
Copyright
© The Authors 2020

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