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The group of diffeomorphisms of a non-compact manifold is not regular

Author

Listed:
  • Jean-Pierre Magnot

    (LAREMA - Laboratoire Angevin de Recherche en Mathématiques - UA - Université d'Angers - CNRS - Centre National de la Recherche Scientifique)

Abstract

We show that a group of diffeomorphisms D on the open unit interval I, equipped with the topology of uniform convergence on any compact set of the derivatives at any order, is non-regular: the exponential map is not defined for some path of the Lie algebra. This result extends to the group of diffeomorphisms of finite dimensional, non-compact manifold M.

Suggested Citation

  • Jean-Pierre Magnot, 2018. "The group of diffeomorphisms of a non-compact manifold is not regular," Post-Print hal-01831632, HAL.
    • Handle: RePEc:hal:journl:hal-01831632
    DOI: 10.1515/dema-2018-0001
    Note: View the original document on HAL open archive server: https://hal.science/hal-01831632
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    Cited by:

    1. Jean-Pierre Magnot, 2019. "On Mathematical Structures On Pairwise Comparisons Matrices With Coefficients In A Group Arising From Quantum Gravity," Post-Print hal-01835958, HAL.
    2. Jean-Pierre Magnot, 2018. "On Mathematical Structures On Pairwise Comparisons Matrices With Coefficients In A Group Arising From Quantum Gravity," Working Papers hal-01835958, HAL.

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