Finite Order Theorems

  • Ivan Kolář
  • Jan Slovák
  • Peter W. Michor
Chapter

Abstract

The purpose of this chapter is to develop a general framework for the theory of geometric objects and operators and to reduce local geometric considerations to finite order problems. In general, the latter is a hard analytical problem and its solution essentially depends on the category in question. Roughly speaking, our methods are efficient when we deal with a sufficiently large class of smooth maps, but they fail e.g. for analytic maps.

Keywords

Filtration Manifold Prool 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Ivan Kolář
    • 1
  • Jan Slovák
    • 1
  • Peter W. Michor
    • 2
  1. 1.Department of Algebra and Geometry, Faculty of ScienceMasaryk UniversityBrnoCzechoslovakia
  2. 2.Institut für MathematikUniversität WienWienAustria

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