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nLab > Latest Changes: C2-equivariant homotopy groups of spheres

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  1. Making a particular page for C_2 equivariant homotopy groups because real Betti realization is fundamental there and doesn’t exist over other groups.

    Natalie Stewart

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeApr 25th 2024
    • (edited Apr 25th 2024)

    I have added more hyperlinks to the first sentence.

    By the way, for pointing to anchors in another page, such as

      [Betti realization](https://ncatlab.org/nlab/show/motivic+homotopy+theory#RealizationFunctors)

    you can omit the domain- and top path name and just type

      [Betti realization](motivic+homotopy+theory#RealizationFunctors)

    diff, v3, current

    • CommentRowNumber3.
    • CommentAuthorAli Caglayan
    • CommentTimeApr 25th 2024
    • (edited Apr 25th 2024)

    Wouldn’t it be better to call this ℤ 2\mathbb{Z}_2-equivariant? Or rather why are these called C 2C_2 rather than ℤ 2\mathbb{Z}_2?

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeApr 25th 2024
    • (edited Apr 25th 2024)

    The notation “ℤ p\mathbb{Z}_p” is used both for (prime) cyclic groups as well for rings of pp-adic numbers.

    For that reason, fields that use both of these notions (such as algebraic topology) tend to disambiguate by using other notation for the cyclic groups.

    Which makes sense, because the canonical notation for the cyclic group as a quotient is rather “ℤ/p\mathbb{Z}\!/\!p” anyways, and since “C” works well for “cyclic”.

  5. Starting to add the relationship between RO(C2)-graded and Z-graded Mackey functor homotopy groups

    Natalie Stewart

    diff, v6, current

  6. Removing the underscore from the name

    Natalie Stewart

    diff, v7, current

1 to 6 of 6

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