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nLab > Latest Changes: The Music of the Spheres

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeFeb 5th 2016

    created The Music of the Spheres, following Ravenel.

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeFeb 5th 2016

    Shame the publisher’s views won out.

    I added to something to The Republic.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeFeb 5th 2016

    Thanks! I have added a little bit.

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeJun 9th 2016

    What am I missing? Music of the Spheres has a link to be created ’Platonic solids’ and yet there’s a redirect for that at Platonic solid.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJun 9th 2016

    Must be some bug with the redirects. I have fixed it (worked around it) by adding explicit pointers to the entry.

    • CommentRowNumber6.
    • CommentAuthorfastlane69
    • CommentTimeJun 9th 2016

    Pardon me, but in what context are you using “chromatic”?

    In music, it refers to twelve notes (the chromatic scale).

    In art, it refers to a continuous spectrum of colors.

    Is it one of these or another meaning being used?

    • CommentRowNumber7.
    • CommentAuthorDavidRoberts
    • CommentTimeJun 9th 2016

    From chromatic homotopy theory:

    By the construction of complex oriented cohomology theories from formal groups (via the Landweber exact functor theorem), the height filtration of formal groups induces a “chromatic” filtration on complex oriented cohomology theories. Chromatic homotopy theory is the study of stable homotopy theory and specifically of complex oriented cohomology theories by means of and along this chromatic filtration.

    • CommentRowNumber8.
    • CommentAuthorMike Shulman
    • CommentTimeJun 9th 2016

    I’ve never really understood where the word “chromatic” comes from here. The best I’ve heard is something like “it decomposes the stable homotopy groups of spheres analogously to how a prism decomposes white light into many colors” which seems like a very tenuous analogy to me.

    • CommentRowNumber9.
    • CommentAuthorDavid_Corfield
    • CommentTimeJun 10th 2016

    There’s the link between chromatic levels and v nv_n-periodicity, so that there can be cases of ’redshift’, as in Rognes’ Introduction to redshift

    Since the v n+kv_{n+k}-periodic families have longer periods, or longer wavelength, than the v nv_n-periodic families, we refer to this as a redshift phenomenon.

    I guess we could do with something on periodic families.

    • CommentRowNumber10.
    • CommentAuthorDavid_Corfield
    • CommentTimeJun 10th 2016

    Of course, saying such a thing, one should start a page. But I see we have periodic map. I fixed some type-setting issues, but it needs greater attention, e.g, there’s a comment “I’m not sure that this is entirely correct”.

    And does it still need a periodic family page?

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