Topology of the diffeomorphism group

  1. I would like to study the path components (isotopy classes) of the diffeomorphism group of some compact Riemann surface. To make sense of path connectedness, I require a notion of continuity; hence, I require a notion of an open set of diffeomorphisms. What sort of topology should I put on the diffeomorphism group?
  2. jcsd
  3. Office_Shredder

    Office_Shredder 4,487
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  4. quasar987

    quasar987 4,773
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    The classical reference is

    Augustin Bangaya, The Structure of Classical Diffeomorphism Groups
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