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nLab > HoTT: Latest Changes: HoTT: homotopy groups of spheres

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  1.  
    • CommentRowNumber1.
    • CommentAuthorAli Caglayan
    • CommentTimeSep 14th 2018

    I have added some ideas that get me out of bed in the morning to the homotopy groups of spheres page. I will try to improve this page a bit too.

    diff, v6, current

    • CommentRowNumber2.
    • CommentAuthorAli Caglayan
    • CommentTimeSep 14th 2018
    I have added a table linking the current results.
    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeSep 14th 2018

    have added cross-links with homotopy groups of spheres (nlab)

    • CommentRowNumber4.
    • CommentAuthorAli Caglayan
    • CommentTimeOct 17th 2018

    Got rid of my terrible attempt at a coloured table. If anybody would like to help me colour it in like on Wikipedia I would be most greatful.

    diff, v12, current

    • CommentRowNumber5.
    • CommentAuthorAlexisHazell
    • CommentTimeOct 18th 2018

    Convert table to HTML, with coloured table cells.

    diff, v13, current

  6. I can try to tweak things to get the mathematics to render later.

    • CommentRowNumber7.
    • CommentAuthorAlexisHazell
    • CommentTimeOct 18th 2018

    Convert Instiki links in table to HTML links.

    diff, v15, current

    • CommentRowNumber8.
    • CommentAuthorAlexisHazell
    • CommentTimeOct 18th 2018
    • (edited Oct 18th 2018)

    Close unclosed <a> tags.

    diff, v15, current

    • CommentRowNumber9.
    • CommentAuthorAlexisHazell
    • CommentTimeOct 18th 2018
    • (edited Oct 18th 2018)

    Remove spurious </a> tag.

    diff, v15, current

    • CommentRowNumber10.
    • CommentAuthorDavidRoberts
    • CommentTimeOct 18th 2018

    Well, that broke the announcement mechanism!

    • CommentRowNumber11.
    • CommentAuthorAlexisHazell
    • CommentTimeOct 18th 2018

    Sorry about the comment spam here as I worked on converting the Instiki table to an HTML table! (I couldn’t see ’preview’ functionality to let me check my changes before submitting?) At any rate, the conversion is now done; but if people aren’t happy with the result, feel free to revert it to the Instiki-table version.

    • CommentRowNumber12.
    • CommentAuthorRichard Williamson
    • CommentTimeOct 18th 2018
    • (edited Oct 18th 2018)

    Fantastic! Thanks very much for this! Funnily enough, you have implemented the mathematics in exactly the same way as I am doing in my work-in-progress tool which parses iTeX/LaTeX to HTML. I take encouragement from this :-)!

    Regarding #10: it is not really the announcement mechanism that broken, rather than that the nForum cannot handle it (i.e. it would break in the same way if one wrote the same directly in the nForum). If one escapes the <a> as code, like I am doing here, it should work again. Perhaps you could edit #8 and #9 in this way, Alexis, just so that they display?

    Regarding #11: indeed, there is no preview, the philosophy of Instiki is that one edits after submitting until happy (there is a 30 minute window after editing where changes are merged into the same edit).

    • CommentRowNumber13.
    • CommentAuthorAli Caglayan
    • CommentTimeOct 18th 2018

    Thank you very much, this is looking great! The colouring will need to be transposed. I should make it more clear that the table has entries pi n(S k)pi_n(S^k), but it is difficult to be very expressive with these tables quickly.

    • CommentRowNumber14.
    • CommentAuthorDavidRoberts
    • CommentTimeOct 18th 2018

    The higher pi n(S 1)pi_n(S^1) should probably be linked, since they should be known from *→S 1\ast \to S^1 being the universal cover (and so give isos on π n\pi_n, n≥2n\geq 2), but I don’t know if this was written down. I haven’t checked Mike’s proof, or any other, that π 1(S 1)=ℤ\pi_1(S^1)=\mathbb{Z}.

    • CommentRowNumber15.
    • CommentAuthorAlexisHazell
    • CommentTimeOct 18th 2018

    Table colouring fixes.

    diff, v16, current

    • CommentRowNumber16.
    • CommentAuthorAlexisHazell
    • CommentTimeOct 18th 2018

    Re. #12:

    Fantastic! Thanks very much for this!

    Thank you for your kind words!

    Funnily enough, you have implemented the mathematics in exactly the same way as I am doing in my work-in-progress tool which parses iTeX/LaTeX to HTML. I take encouragement from this :-)!

    :-)

    it is not really the announcement mechanism that broken, rather than that the nForum cannot handle it (i.e. it would break in the same way if one wrote the same directly in the nForum). If one escapes the &l;a> as code, like I am doing here, it should work again. Perhaps you could edit #8 and #9 in this way, Alexis, just so that they display?

    I’ve now made those changes; thanks for the heads-up.

    Regarding #11: indeed, there is no preview, the philosophy of Instiki is that one edits after submitting until happy (there is a 30 minute window after editing where changes are merged into the same edit).

    Ah, okay.

    • CommentRowNumber17.
    • CommentAuthorAlexisHazell
    • CommentTimeOct 18th 2018

    Re. #13:

    You’re welcome. :-) But, gah, sorry about the colouring errors! I’ve now changed the table so that the colours match the colours of the relevant entries in the Wikipedia table.

1 to 17 of 17

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