Volume 18, issue 4 (2018)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Refinements of the holonomic approximation lemma

Daniel Álvarez-Gavela

Algebraic & Geometric Topology 18 (2018) 2265–2303
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