#### Volume 18, issue 4 (2018)

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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 $h\phantom{\rule{0.3em}{0ex}}$–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