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nLab > Latest Changes: little cubes operad

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeNov 4th 2018

    added statement of and references to the weak equivalence with the Fulton-MacPherson operad (here)

    added the same statement also at Fulton-MacPherson operad

    diff, v32, current

    • CommentRowNumber2.
    • CommentAuthorDmitri Pavlov
    • CommentTimeAug 3rd 2021

    Added redirects: E_n-operad

    diff, v40, current

    • CommentRowNumber3.
    • CommentAuthorHurkyl
    • CommentTimeNov 18th 2021
    • (edited Nov 18th 2021)

    The statement that Rect(□ k×S,□ k)Rect(\square^k \times S, \square^k ) can be identified with an open subset of (ℝ 2k) S(\mathbb{R}^{2k})^S is wrong, isn’t it?

    For example, Rect(□ 1,□ 1)Rect(\square^1, \square^1) can be identified with the set of pairs (a,b)(a,b) satisfying 0<a≤10 \lt a \leq 1, |b|≤1−a|b| \leq 1-a, which is a triangle that includes part of its boundary.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeNov 19th 2021
    • (edited Nov 19th 2021)

    I suppose this is about this Definition (which, somewhat awkwardly, somebody had copied verbatim from HA p. 758; I have now at least added some hyperlinks and touched the formatting and wording).

    diff, v41, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeNov 19th 2021

    Regarding the point you raise: Scanning through Higher Algebra, it looks like the identity map is meant to count as a rectilinear embedding (explicit in Ex. 5.1.0.6, p. 759), while would-be open-ness of the space of rectilinear embedding seems not to be used. That makes me think that the “open subset” on p. 758 is a glitch and that the line was just meant to say that Rect(−,−)Rect(-,-) is equipped with the subspace topology.

    • CommentRowNumber6.
    • CommentAuthorHurkyl
    • CommentTimeNov 19th 2021
    • (edited Nov 19th 2021)

    Oh good; I’m not missing something and it’s harmless. Since I’ve just started trying to digest the little cubes operad and still find it somewhat opaque I really didn’t feel confident just removing that line.

    • CommentRowNumber7.
    • CommentAuthorDmitri Pavlov
    • CommentTimeFeb 17th 2023

    Added:

    A comprehensive reference for many known models is

    diff, v42, current

1 to 7 of 7

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