Refinements of the holonomic approximation lemma

Daniel Álvarez-Gavela

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)2265-2303
Number of pages39
JournalAlgebraic and Geometric Topology
Issue number4
StatePublished - Apr 26 2018

All Science Journal Classification (ASJC) codes

  • Geometry and Topology


  • Cutoff
  • Flexibility
  • Flexible
  • Holonomic approximation
  • h-principle


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