Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory object of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).

nLab > Latest Changes: proper action

Bottom of Page

1 to 7 of 7

  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

  1.