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nLab > Latest Changes: associahedron

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeDec 17th 2009

    Jim Stasheff pointed out a reference that discusses categorifications of associahedra. I added the ref to associahedron

    • CommentRowNumber2.
    • CommentAuthorColin Tan
    • CommentTimeMay 9th 2014

    Urs, this link at associahedron to the reference by Forcey you mentioned is currently broken.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMay 9th 2014

    Colin, with broken links, Google is your friend. Here it gives us this:

    • Stefan Forcey, Quotients of the multiplihedron as categorified associahedra, Homology Homotopy Appl. Volume 10, Number 2 (2008), 227-256. (Euclid)
    • CommentRowNumber4.
    • CommentAuthorTodd_Trimble
    • CommentTimeMar 17th 2015

    I have added an abstract description of (barycentrically subdivided) associahedra, in terms of a bar construction, to the definition section of associahedron. This is actually a definition, which wasn’t really there before.

    • CommentRowNumber5.
    • CommentAuthorMike Shulman
    • CommentTimeMar 17th 2015

    Nice!

  6. I added a pointer/short description of Loday’s concrete realization of the associahedron as a convex hull of integer coordinates. I wonder how it relates to the construction Todd gave above?

    • CommentRowNumber7.
    • CommentAuthorTodd_Trimble
    • CommentTimeNov 25th 2015

    Good question. I believe Stefan Forcey has worked on bridging these sorts of abstract and concrete descriptions of polyhedra that arise in operadic combinatorics. You’re right that some effort to go into this should be entered at the nLab.

  8. The links under “Rotatable illustrations of some Stasheff polyhedra…” seem to be dead. I could be wrong, so I won’t remove them, although I did explore them and could not find rotatable polyhedra. For separate reasons I recently made a 3D rotatable associahedra app for the first 10 associahedra, and given that these links seem to be dead, I thought I would share.

    Anonymous

    diff, v30, current

  9. That app is very cool! Thanks for adding! It brings home the impossibility of dealing with higher categories purely combinatorically! I agree that we can tweak the old links, I will do that now.

    • CommentRowNumber10.
    • CommentAuthorRichard Williamson
    • CommentTimeOct 17th 2020
    • (edited Oct 17th 2020)

    Updating and otherwise tweaking links to visualisations of Stasheff polyhedra, giving preference to the fantastic app linked to in the previous edit!

    diff, v31, current

  11. The picture of K 4K_4 doesn’t display too well on a mobile. We should replace it by a Tikz figure; I think I have already created such a figure somewhere else on the nLab, I’ll see if I can find it later (or someone else is welcome to do so if they have time!).

    • CommentRowNumber12.
    • CommentAuthorJohn Baez
    • CommentTimeSep 11th 2022
    • (edited Sep 11th 2022)
    There's something funny about the picture of the pentagon identity here: at least for me, the right-hand end of each bracketed expression is blanked out, like

    $((w \otimes x) \otimes y) \otimes $
    • CommentRowNumber13.
    • CommentAuthorUrs
    • CommentTimeSep 11th 2022

    I have replaced the pentagon diagram (here) with a tikzcd-rendering (copied from pentagon identity)

    diff, v32, current

  14. Adding reference

    Anonymouse

    diff, v35, current

1 to 14 of 14

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