Volume 25, issue 6 (2021)

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The Legendrian Whitney trick

Roger Casals, Dishant M Pancholi and Francisco Presas

Geometry & Topology 25 (2021) 3229–3256

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.

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contact structure, isocontact embeddings, $h$–principle
Mathematical Subject Classification
Primary: 53D10
Secondary: 53D15, 57R17
Received: 15 June 2020
Revised: 12 October 2020
Accepted: 13 November 2020
Published: 30 November 2021
Proposed: Leonid Polterovich
Seconded: Yasha Eliashberg, András I Stipsicz
Roger Casals
Department of Mathematics
University of California, Davis
Davis, CA
United States
Dishant M Pancholi
Institute for Mathematical Sciences
Francisco Presas
Instituto de Ciencias Matemáticas