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nLab > Latest Changes: coset space coprojection admitting local sections

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeApr 4th 2021
    • (edited Apr 4th 2021)

    am giving this its own entry, in order to record sufficient conditions on topological subgroup inclusions H⊂GH \subset G for the coset space coprodoction G→G/HG \to G/H to admit local sections.

    So far I have two original references here (Gleason 50, Mostert 53). One should add some textbook account, too.

    Am also referencing this at closed subgroup, at coset space and maybe elsewhere.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeApr 4th 2021
    • (edited Apr 4th 2021)

    at coset space it is claimed (I guess this was myself) that the proof for compact Lie subgroups is due to

    But scanning through this article now, I haven’t spotted yet where that statement would appear in this article.

    v1, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeApr 4th 2021

    changed page name from “… with local sections” to “… admitting local sections”

    v1, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeApr 4th 2021

    changed page name to singular

    diff, v2, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeApr 12th 2021

    I have added pointer to Section 3 of

    • Takashi Karube, On the local cross-sections in locally compact groups, J. Math. Soc. Japan 10(4): 343-347 (October, 1958) (doi:10.2969/jmsj/01040343)

    for mentioning of one and a half counter-examples.

    Any larger collection of counter-examples out there?

    diff, v4, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeSep 6th 2021
    • (edited Sep 6th 2021)

    added pointer also to:

    Tammo tom Dieck, Theodor Bröcker, Thm. 4.3 on p. 33 of: *Representations of compact Lie groups, Springer 1985 (doi:10.1007/978-3-662-12918-0)

    diff, v5, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeSep 6th 2021
    • (edited Sep 6th 2021)

    also included this into the statement of the proposition (here)

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeSep 19th 2021
    • (edited Sep 19th 2021)

    added (here) the example U(ℋ)→U(ℋ)/S 1≃PU(ℋ)\mathrm{U}(\mathcal{H}) \to \mathrm{U}(\mathcal{H})/S^1 \,\simeq\, PU(\mathcal{H})

    diff, v7, current

1 to 8 of 8

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