• 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}
}```
• Published 23 January 2001
• Mathematics
• arXiv: Symplectic Geometry
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

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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
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• Mathematics
• 2001
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,
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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
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• Mathematics, Philosophy
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We give a short proof of Gromov’s theorem on directed embeddings [1; 2.4.5 (C′)]. AMS Classification 57R40, 57R42; 57A05
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1. A Survey of Basic Problems and Results.- 2. Methods to Prove the h-Principle.- 3. Isometric C?-Immersions.- References.- Author Index.