Refinements of the holonomic approximation lemma

Álvarez-Gavela, Daniel

doi:10.2140/agt.2018.18.2265

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Refinements of the holonomic approximation lemma

Daniel Álvarez-Gavela

Algebraic & Geometric Topology 18 (2018) 2265–2303

DOI: 10.2140/agt.2018.18.2265

Abstract

The holonomic approximation lemma of Eliashberg and Mishachev is a powerful tool in the philosophy of the $h$ –principle. By carefully keeping track of the quantitative geometry behind the holonomic approximation process, we establish several refinements of this lemma. Gromov’s idea from convex integration of working “one pure partial derivative at a time” is central to the discussion. We give applications of our results to flexible symplectic and contact topology.

Keywords

h-principle, holonomic approximation, flexible, flexibility, cutoff

Mathematical Subject Classification 2010

Primary: 53DXX, 57R99

Secondary: 57R45, 57R17

References

Publication

Received: 6 April 2017

Revised: 1 January 2018

Accepted: 16 January 2018

Published: 26 April 2018

Authors

Daniel Álvarez-Gavela
Department of Mathematics Stanford University Stanford, CA United States

Volume 18, issue 4 (2018)