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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeFeb 13th 2019

    a minimum, for the moment just so as to record some references on Pin(2)Pin(2)-equivariant homotopy theory (as kindly pointed out by David Roberts)

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeFeb 13th 2019

    added this little diagram:

    2D 2n AA Pin (2) AA Spin(3) (pb) (pb) D 2n AA O(2) AA SO(3) \array{ 2 D_{2n} &\overset{\phantom{AA}}{\hookrightarrow}& Pin_-(2) &\overset{\phantom{AA}}{\hookrightarrow}& Spin(3) \\ \big\downarrow &{}^{(pb)}& \big\downarrow &{}^{(pb)}& \big\downarrow \\ D_{2n} &\overset{\phantom{AA}}{\hookrightarrow}& O(2) &\overset{\phantom{AA}}{\hookrightarrow}& SO(3) }

    v1, current

    • CommentRowNumber3.
    • CommentAuthorDavid_Corfield
    • CommentTimeFeb 13th 2019

    There’s a Pin +(2)Pin_{+}(2) group as well, I take it. Is either of them the default when Pin(2)Pin(2) is mentioned?

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeFeb 13th 2019

    Yes, there is Pin +(2)Pin_+(2), obtained by changing the square of the reflection generator from 1-1 to +1. I focused on Pin (2)Pin_-(2) just because that’s the choice that fits into the story of the finite subgroups of SU(2). But if anyone has the energy, it would be good to add discussion of Pin +(2)Pin_+(2), too.

  1. added a (very) brief explanation for why Pin(2)-equivariant things appear in topology, and a reference to Furuta’s paper

    Arun Debray

    diff, v8, current

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