Haefliger structures and symplectic/contact structures
Copyright policy )Haefliger structures and symplectic/contact structures
For some geometries including symplectic and contact structures on an n -dimensional manifold, we introduce a two-step approach to Gromov’s h -principle. From formal geometric data, the first step builds a transversely geometric Haefliger structure of codimension n . This step works on all manifolds, even closed. The second step, which works only on open manifolds and for all geometries, regularizes the intermediate Haefliger structure and produces a genuine geometric structure. Both steps admit relative parametric versions. The proofs borrow ideas from W. Thurston, like jiggling and inflation. Actually, we are using a more primitive jiggling due to R. Thom.
- Université de Bretagne Occidentale France
- Université de Nantes France
- University of Western Brittany France
- Sciences Po France
- University of Southern Brittany France
immersion, Haefliger’s Γ-structures, Symplectic and contact topology in high or arbitrary dimension, MSC 57R17, submersion, Foliations, 510, Mathematics - Geometric Topology, [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT], 57R30, FOS: Mathematics, Foliations in differential topology; geometric theory, inflation, Haefliger's \(\Gamma\)-structures, [MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT], foliations, contact structure, jiggling, Geometric Topology (math.GT), [MATH.MATH-SG]Mathematics [math]/Symplectic Geometry [math.SG], [MATH.MATH-SG] Mathematics [math]/Symplectic Geometry [math.SG], symplectic structure, Mathematics - Symplectic Geometry, Symplectic Geometry (math.SG)
immersion, Haefliger’s Γ-structures, Symplectic and contact topology in high or arbitrary dimension, MSC 57R17, submersion, Foliations, 510, Mathematics - Geometric Topology, [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT], 57R30, FOS: Mathematics, Foliations in differential topology; geometric theory, inflation, Haefliger's \(\Gamma\)-structures, [MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT], foliations, contact structure, jiggling, Geometric Topology (math.GT), [MATH.MATH-SG]Mathematics [math]/Symplectic Geometry [math.SG], [MATH.MATH-SG] Mathematics [math]/Symplectic Geometry [math.SG], symplectic structure, Mathematics - Symplectic Geometry, Symplectic Geometry (math.SG)
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).5 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!