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

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

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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.

Keywords: diffeology; diffeomorphisms; infinite dimensional Lie groups; exponential map (search for similar items in EconPapers)
Date: 2018-01-25
Note: View the original document on HAL open archive server: https://hal.science/hal-01831632v1
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Citations: View citations in EconPapers (2)

Published in Demonstratio Mathematica, 2018, 51 (1), pp.8 - 16. ⟨10.1515/dema-2018-0001⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01831632

DOI: 10.1515/dema-2018-0001

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