Isomorphisms between Diffeomorphism Groups

  • Augustin Banyaga
Part of the Mathematics and Its Applications book series (MAIA, volume 400)


In his “Erlanger Programme” (1872) [87], Klein defined a geometry of a set X as the study of thoses properties of “figures” (subsets of X) which remain invariant under a group G(X) of transformations of X. Here let us quote Greenberg’s beautiful book [66] on “Euclidean and non Euclidean Geometries,” p. 213 Invariance and groups are the unifying concepts in Klein’s Erlanger Programme. Groups of transformations had been used in geometry for many years, but Klein’s originality consisted in reversing the roles, in making the group the primary object of interest and letting it operate on variuous geometries, looking for invariants. Klein proposed to translate geometric problems in projective geometry into algebraic problems in invariant theory.


Vector Field Symplectic Form Smooth Manifold Symplectic Manifold Symplectic Case 
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Copyright information

© Springer Science+Business Media Dordrecht 1997

Authors and Affiliations

  • Augustin Banyaga
    • 1
  1. 1.Department of MathematicsThe Pennsylvania State UniversityUSA

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