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nLab > Latest Changes: d-invariant

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeDec 2nd 2020

    Just for completeness, to go with e-invariant and f-invariant.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeDec 2nd 2020

    We don’t yet have a page for f-invariant.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeDec 7th 2020

    spelled out (here) the example of how the d-invariant specializes to the ordinary Hopf degree.

    Am adding this example now also to degree of a continuous function and to Hopf degree theorem

    diff, v5, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJan 15th 2021
    • (edited Jan 15th 2021)

    I have added a section “Trivializations of the d-invariant” (here) with some observations.

    While from a modern abstract homotopy-theoretic perspective this is really a one-line observation, unwinding this accounts for (and completes) a fair bit of argument in Section 16 of Conner-Floyd’s 66 book (for which no modernized account seems to exist?!), and it also sets the pattern for the other classical constructions of the e-invariant and the Hopf invariant.

    So therefore I thought it would be useful to spell this out a little. Also, this section provides details now linked to at MUFr and at Adams e-invariant – Construction via unit cofiber cohomology theories.

    diff, v6, current

    • CommentRowNumber5.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 15th 2021

    Some new candidates for a HoTT treatment?

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJan 15th 2021

    I had had that same thought, yes. The style of construction that I am writing out at Adams e-invariant – Construction via cofiber theories should lends itself to full formalization in HoTT. For instance the Conner-Floyd theorem becomes a formal corollary by factoring a homotopy pasting diagram (here) .

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeJan 15th 2021

    have added the diagrams for the “quick abstract proof” (here)

    diff, v7, current

1 to 7 of 7

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