• Corpus ID: 119160087

Holonomic approximation and Gromov's h-principle

  title={Holonomic approximation and Gromov's h-principle},
  author={Yakov M. Eliashberg and Nikolai M. Mishachev},
  journal={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… 
René Thom and an Anticipated h-Principle
The first part of this article intends to present the role played by Thom in diffusing Smale's ideas about immersion theory, at a time (1957) where some famous mathematicians were doubtful about
h-Principle for Stratified Spaces
. We extend Gromov and Eliashberg-Mishachev’s h − principle on manifolds to stratified spaces. This is done in both the sheaf-theoretic framework of Gromov and the smooth jets framework of
Fibration structure for Gromov h-principle
The h-principle is a powerful tool for obtaining solutions to partial differential inequalities and partial differential equations. Gromov discovered the h-principle for the general partial
Holonomic approximation through convex integration
Convex integration and the holonomic approximation theorem are two well-known pillars of flexibility in differential topology and geometry. They may each seem to have their own flavor and scope. The
Maps of manifolds of the same dimension with prescribed Thom-Boardman singularities
In this paper we extend Y.Eliashberg's $h$-principle to arbitrary generic smooth maps of smooth manifolds. Namely, we prove a necessary and sufficient condition for a continuous map of smooth
The Golden Age of Immersion Theory in Topology: 1959-1973
We briefly review selected contributions to immersion-theoretic topology, from S. Smale's immersion theory for spheres to M. Gromov's convex integration theory, during the early "golden" period from
J-holomorphic Curves And Periodic Reeb Orbits
We study the $J-$holomorphic curves in the symplectization of the contact manifolds and prove that there exists at least one periodic Reeb orbits in any closed contact manifold with any contact form
An application of the h-principle to manifold calculus
  • Apurv Nakade
  • Mathematics
    Journal of Homotopy and Related Structures
  • 2020
Manifold calculus is a form of functor calculus that analyzes contravariant functors from some categories of manifolds to topological spaces by providing analytic approximations to them. In this
A note on symplectic topology of $b$-manifolds
A Poisson manifold $(M^{2n},\p)$ is $b$-symplectic if $\bigwedge^n\p$ is transverse to the zero section. In this paper we apply techniques native to Symplectic Topology to address questions
Symplectic topology and b-symplectic structures
Therefore symplectic structures on a fixed (even) dimension have no local invariants; this is also reflected in having an infinite dimensional group of symmetries: infinitesimal symmetries are vector


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,
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