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nLab > Latest Changes: equivariant triangulation theorem

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeFeb 19th 2019

    A minimum, for the moment just so as to record the articles by Illman

    v1, current

    • CommentRowNumber2.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJul 9th 2022

    Added:

    These results continue to hold when GG is not compact, see \cite{Illman00}.

    • {#Illman00} Sören Illman, Existence and uniqueness of equivariant triangulations of smooth proper G-manifolds with some applications to equivariant Whitehead torsion, J. Reine Angew. Math. 524 (2000), 129–183. doi.

    diff, v7, current

    • CommentRowNumber3.
    • CommentAuthorDavid_Corfield
    • CommentTimeJul 10th 2022

    How does comparison with the plain case, triangulation theorem, look with regard to:

    Conversely, deep theorems assert that a given kind of triangulation does not generally exists for a given class of manifolds.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJul 10th 2022
    • (edited Jul 10th 2022)

    My understanding is that the equivariant case is much harder and that there is not essentially more work on it than listed in the entry (good though that Dmitri found one more reference previously missing), which all focuses on (equivariant) smooth triangulations of smooth manifolds.

    Of course, a trivial thing to be said is that when a given type of ordinary triangulation does not exist, then an equivariant version won’t exist either.

    • CommentRowNumber5.
    • CommentAuthorDavid_Corfield
    • CommentTimeJul 10th 2022

    There are some remarks at MO here.

1 to 5 of 5

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