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nLab > Latest Changes: proper action

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeApr 24th 2018

    the minimum definition and some plain cross-links (we didn’t have this elsewhere, or do we?)

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeOct 21st 2020

    added the example that every smooth action of a compact Lie group on a smooth manifold is proper (here)

    diff, v4, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeApr 13th 2021

    I have expanded the definition section a little, added mentioning of alternative definitions to the shear map being proper (“Bourbaki properness”), namely Palais’ definition in one of its many forms (“Palais properness”) highlighted the need of local compactness for these to be equivalent, added pointer to the original article by Palais, mentioned his attribution of the concept to Borel. Also pointer to Bourbaki, but didn’t actually look that up.

    diff, v8, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeApr 13th 2021
    • (edited Apr 13th 2021)

    also added “Borel properness”, i.e.: the subset of GG not translating a given compactum KK away from itself is compact (Palais60 on p. 303 attributes this to unpublished work of Borel)

    diff, v8, current

    • CommentRowNumber5.
    • CommentAuthorGuest
    • CommentTimeNov 16th 2022

    added the example that every smooth action of a compact Lie group on a smooth manifold is proper (here)

    diff, v4, current

    The reference is wrong, I do not find anything in Cor. 7.2 of Lee (either of the cited books), moreover the statement is obvious for any action of a compact topological group, without any smoothness…

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeNov 16th 2022

    Thanks for the alert. Not sure what happened here.

    I have now changed “smooth” to “continuous” and “7.2” to “21.6”.

    diff, v13, current

  7. Fixed a minor typo in the definition of Palais properness (U instead of V)

    Cin

    diff, v14, current

1 to 7 of 7

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