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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeNov 4th 2013

    added the plain traditional definition to J-homomorphism

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeNov 4th 2013

    have added the statement of the Adams cojecture to J-homomorphism.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeNov 4th 2013

    have copied that paragraph also into the entry stable homotopy groups of spheres (which is badly in need of some genuine content)

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeNov 4th 2013
    • (edited Nov 4th 2013)

    have added the list of values of |J(π 4k1(O))|\vert J(\pi_{4k-1}(O))\vert for low kk.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeNov 11th 2013
    • (edited Nov 11th 2013)

    I have added some more comments to J-homomorphism – Definition – On groups meant to be careful about the argument of how the continuous action of the topological group O(n)O(n) on the topological space S nS^n turns into an \infty-action of the homotopy type of the stable orthogonal group on the sphere spectrum.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeNov 12th 2013

    added the characterization of the image of J in terms of chromatic homotopy theory (in the E(1)E(1)-local sphere spectrum) to Image of J – In terms of chromatic homotopy theory

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeNov 17th 2013
    • (edited Nov 17th 2013)

    added a few more pointers to discussion of the image of J in terms of K(1)K(1)/E(1)E(1)-localization of the sphere spectrum:

    Is there anything else?

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeSep 30th 2014

    added pointer to Gaudens-Menichi 07 for expressing the canonical O(n)O(n)-action on general nn-fold loop spaces in terms of the J-homomorphisms.

    If anyone has more pointers for this, let me know.

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeMar 21st 2019

    added pointer to

    • Arpon Raksit, Vector fields and the J-homomorphism, 2014 (pdf)

    diff, v38, current

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeOct 9th 2020
    • (edited Oct 9th 2020)

    I have added pointer to

    But I am looking for a citeable reference on the J-homomorphism as a map of spectra

    koJPic(𝕊). ko \overset{\;\;\;\;J\;\;\;\;}{\longrightarrow} Pic(\mathbb{S}) \,.

    Westerland’s slides mention this on p. 5. But is there a citeable account that goes with this?

    diff, v41, current

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeOct 9th 2020

    added pointer to

    • Dustin Clausen, pp-adic J-homomorphisms and a product formula (arXiv:1110.5851)

    where the statement is in Section 2.

    diff, v41, current

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeNov 28th 2020

    added pointer to:

    diff, v43, current

    • CommentRowNumber13.
    • CommentAuthorUrs
    • CommentTimeNov 29th 2020

    added pointer to:

    diff, v44, current

    • CommentRowNumber14.
    • CommentAuthorJohn Baez
    • CommentTimeDec 10th 2020


    homotopy groups ±1π n(S n)\pm 1 \in \pi_n(S^n).


    homotopy classes ±1π n(S n)\pm 1 \in \pi_n(S^n)

    diff, v45, current

    • CommentRowNumber15.
    • CommentAuthorDavid_Corfield
    • CommentTimeDec 12th 2020

    Corrected the link for Lorman’s slides.

    diff, v46, current

    • CommentRowNumber16.
    • CommentAuthorUrs
    • CommentTimeDec 14th 2020

    added pointer to:

    diff, v47, current