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nLab > Latest Changes: Pontryagin-Thom construction -- references

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeDec 23rd 2020
    • (edited Dec 23rd 2020)

    this is a bare list of references, to be !include-ed into relevant entries

    (various parts of this list have been contained at Cohomotopy, Cohomotopy charge map, Thom’s theorem, Pontryagin-Thom construction and elsewhere; this here now to ease harmonizing/completing these lists)

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeFeb 4th 2021
    • (edited Feb 4th 2021)

    added pointer to:

    diff, v10, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeFeb 4th 2021

    added pointer to:

    diff, v11, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeFeb 5th 2021

    added pointer to:

    diff, v13, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeFeb 26th 2021

    added this pointer:

    The Pontrjagin theorem must have been known to Pontrjagin at least by 1936, when he announced the computation of the second stem of homotopy groups of spheres:

    • Lev Pontrjagin, Sur les transformations des sphères en sphères (pdf) in: Comptes Rendus du Congrès International des Mathématiques – Oslo 1936 (pdf)

    diff, v14, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeFeb 27th 2021

    I have added pointer to Theorem C in

    which seems to be the first place where the “Pontryagin-Thom theorem”, stably and for general tangential structure, is actually stated.

    diff, v15, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeMar 3rd 2021

    added section (here) with references on generalization of the Pontrjagin theorem to a twisted/equivariant Pontrjagin theorem.

    (Currently the only items are Cruikshank’s, but maybe to be expanded)

    diff, v16, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeMar 3rd 2021

    added a sub-section “Pontrjagin’s construction – In negative codimension” (here) with pointers to the “May-Segal theorem” (identifying Cohomotopy cocycle spaces with configuration spaces of points)

    (I should really give May-Segal theorem it’s own entry, since it’s somewhat buried at configuration space of points. But not right now.)

    diff, v16, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeMar 3rd 2021
    • (edited Mar 3rd 2021)

    for what it’s worth, on the twisted Pontrjagin theorem (here) I have changed the wording from “straightforward generalization” to “fairly straightforward generalization” and added pointer to Cruickshanks’ Lemma-like Section 5.1, which, after all, takes him a full page.

    diff, v17, current

  10. fix title of Milnor book

    Anonymous

    diff, v19, current

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeJun 8th 2023

    added pointer to:

    diff, v20, current

1 to 11 of 11

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