• Corpus ID: 119160087

Holonomic approximation and Gromov's h-principle

@article{Eliashberg2001HolonomicAA,
  title={Holonomic approximation and Gromov's h-principle},
  author={Yakov M. Eliashberg and Nikolai M. Mishachev},
  journal={arXiv: Symplectic Geometry},
  year={2001}
}
In 1969 M. Gromov in his PhD thesis greatly generalized Smale-Hirsch-Phillips immersion-submersion theory by proving what is now called the h-principle for invariant open differential relations over open manifolds. Gromov extracted the original geometric idea of Smale and put it to work in the maximal possible generality. Gromov's thesis was brought to the West by A. Phillips and was popularized in his talks. However, most western mathematicians first learned about Gromov's theory from A… 
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References

SHOWING 1-8 OF 8 REFERENCES
Lectures on the theorem of gromov
In his thesis [2], gromov proves a very general theorem which contains as particular cases the Smale-Hirsch theorem on in~nersions [7] and [4] , and Phillips' theorem on submersions [5], as well as
The compression theorem I
This the first of a set of three papers about the Compression Theorem: if M^m is embedded in Q^q X R with a normal vector field and if q-m > 0, then the given vector field can be straightened (ie,
DIRECTED EMBEDDINGS AND THE SIMPLIFICATION OF SINGULARITIES
A theory of simplification of singularities of maps is developed, based on Gromov's convex integration theory. In particular, subject to mild bundle hypotheses, up to a C0-small smooth ambient
Directed embeddings: a short proof of Gromov's theorem
We give a short proof of Gromov’s theorem on directed embeddings [1; 2.4.5 (C′)]. AMS Classification 57R40, 57R42; 57A05
Immersions of manifolds
Immersions of an m-manifold in an n-manifold, n>m, are classified up to regular homotopy by the homotopy classes of sections of a vector bundle E associated to the tangent bundle of M.  When N = Rn ,
Partial Differential Relations
1. A Survey of Basic Problems and Results.- 2. Methods to Prove the h-Principle.- 3. Isometric C?-Immersions.- References.- Author Index.
Submersions of open manifolds