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A Survey of Basic Problems and Results

  • Mikhael Gromov
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE3, volume 9)

Abstract

Consider a C-smooth fibration p: XV and let X (r) be the space of r-jets (of germs) of smooth sections f: VX. Denote by p r : X (r)V and p r s : X ( s )X (r) for s > r ≥ 0, where X (0) \(\mathop{{{\text{ }} = }}\limits^{{def}}\) X, the natural projections. The r th-order jet (or r-jet) of a C r -smooth section f: VX is denoted by J f r : VX (r). A section φ: VX (r) is called holonomic if it is the r-jet of some C r -section f: VX. This f, if it exists, is unique. Namely f = p 0 r φ, since p 0 r J f r = f for all sections f: VX. Thus, sections f: VX are identified with holonomic sections VX (r) by f ↦ J f r .

Keywords

Section Versus Isometric Immersion Manifold Versus Open Manifold Weak Homotopy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Mikhael Gromov
    • 1
  1. 1.Institute des Hautes Etudes ScientifiquesBures-sur-YvetteFrance

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