The Legendrian Whitney trick

Casals, Roger; Pancholi, Dishant M; Presas, Francisco

doi:10.2140/gt.2021.25.3229

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The Legendrian Whitney trick

Roger Casals, Dishant M Pancholi and Francisco Presas

Geometry & Topology 25 (2021) 3229–3256

DOI: 10.2140/gt.2021.25.3229

Abstract

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.

Keywords

contact structure, isocontact embeddings, $h$–principle

Mathematical Subject Classification

Primary: 53D10

Secondary: 53D15, 57R17

References

Publication

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

Authors

Roger Casals
Department of Mathematics University of California, Davis Davis, CA United States

Dishant M Pancholi
Institute for Mathematical Sciences Chennai India

Francisco Presas
Instituto de Ciencias Matemáticas CSIC–UAM–UC3M–UCM Madrid Spain

Volume 25, issue 6 (2021)