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nLab > Latest Changes: chord diagram

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  1. I created a short page for chord diagram, and also added a bit of relevant information to Vassiliev invariant.

    • CommentRowNumber2.
    • CommentAuthorRichard Williamson
    • CommentTimeSep 10th 2018
    • (edited Sep 10th 2018)
    I will fix the included figures on this page shortly.
    • CommentRowNumber3.
    • CommentAuthorRichard Williamson
    • CommentTimeSep 10th 2018
    • (edited Sep 10th 2018)

    Fixed the diagrams now, hopefully. [Edit: there is something strange going on which causes the diagrams not to render correctly after an edit, but to render correctly after I re-render manually. I will look into it when I get the chance, probably this evening.]

    diff, v29, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeNov 20th 2019
    • (edited Nov 20th 2019)

    added these pointers:

    Discussion of chord diagrams encoding SYK model correlators as representing hyperbolic/holographic content:

    • {#BINT18} Micha Berkooz, Mikhail Isachenkov, Vladimir Narovlansky, Genis Torrents, Section 5 of: Towards a full solution of the large NN double-scaled SYK model, JHEP 03 (2019) 079 (arxiv:1811.02584)

    • {#Narovlansky19} Vladimir Narovlansky, Slide 23 (of 28) of: Towards a Solution of Large NN Double-Scaled SYK, Nazareth 2019 (pdf, NarovlanskySYK19.pdf:file)

    following

    diff, v34, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeNov 24th 2019

    In a new Properties section Relation to Chern-Simns diagrams I added pointer to chord diagrams modulo 4T are Chern-Simons diagrams modulo STU.

    No other text yet. To be expanded. But not tonight.

    diff, v37, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeNov 29th 2019

    I have replaced the graphics illustrating a typical chord diagram (first graphics in the entry) with a new one (here) that may be a little more informative

    diff, v46, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeNov 29th 2019

    made explicit the definition of 𝒜 c\mathcal{A}^c (here)

    diff, v47, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeApr 29th 2020

    added pointer to today’s

    diff, v56, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeOct 14th 2020

    added pointer to today’s

    • Ali Assem Mahmoud, Karen Yeats, Connected Chord Diagrams and the Combinatorics of Asymptotic Expansions (arXiv:2010.06550)

    diff, v57, current

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeApr 23rd 2021

    added pointer to these two, which might be close to the earliest appearance of the concept of chord diagrams (?):

    diff, v58, current

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeMay 4th 2021
    • (edited May 4th 2021)

    there is an evident general encoding of hyperbolic tesselations by round chord diagrams.

    Is this made explicit anywhere?

    In particular, I am wondering about the following:

    It should be possible to obtain the round chord diagram for an {n,k}\{n,k\} tesselation at some finite stage by starting with a suitable horizontal chord diagram on n−1n-1 strands, then iteratively “cabling” it into itself and forming vertical composites of that with itself, and finally taking the trace to a round chord diagram with a cyclic permutation.

    Is this described anywhere?

    • CommentRowNumber12.
    • CommentAuthorperezl.alonso
    • CommentTimeSep 14th 2023

    In 1912.10425, intuitively what explains the fact that the physically-meaningful object is the associative algebra of chord diagrams? More precisely, how can we see we can just take the concatenation to be associative, unlike virtually any discussion related to say concatenation of paths (where one has to quotient by homotopy)? Is it because this describes the topological phase space?

    • CommentRowNumber13.
    • CommentAuthorUrs
    • CommentTimeSep 15th 2023

    Yes, because the chord diagram algebra is the Pontrjagin ring of the loop group: The composition in the loop group is only A ∞A_\infty-associative, but under passage to homology this becomes an associative algebra.

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