The Legendrian Whitney trick

Casals, Roger¹ ; Pancholi, Dishant M² ; Presas, Francisco³

¹ Department of Mathematics, University of California, Davis, Davis, CA, United States
² Institute for Mathematical Sciences, Chennai, India
³ Instituto de Ciencias Matemáticas, CSIC–UAM–UC3M–UCM, Madrid, Spain

Geometry & topology, Tome 25 (2021) no. 6, pp. 3229-3256.

Résumé

We prove the Legendrian Whitney trick, which allows for the removal of intersections between codimension-$2$ contact submanifolds and Legendrian submanifolds, assuming such a smooth cancellation is possible. We apply this technique to prove the first known existence $h$–principle for codimension-$2$ isocontact embeddings, with a prescribed arbitrary contact structure on its domain.

Détail

DOI : 10.2140/gt.2021.25.3229

Keywords: contact structure, isocontact embeddings, $h$–principle

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