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    • Changed title and links to different convention, see discussion here. Also updated related concepts.

      Edit: I just realized this didn’t work as there are two seperate articles for 4d TQFT and D=4 TQFT.

      v1, current

    • Created a stub page. It would be good to have an explicit definition of wreath on this page, but I don’t have time right now.

      v1, current

    • I have expanded the Idea-section at 3d quantum gravity and reorganized the remaining material slightly.

      I feel unsure about the pointer to “group field theory” in the References. Can anyone list results that have come out of group field theory that are relevant here?

      I find the following noteworthy, and I am not sure if this is widely appreciated:

      the original discussion of the quantization of 3d gravity by Witten in 1988 happens work out to be precisely along the lines that “loop quantum gravity” once set out to get to work in higher dimensions: one realizes

      1. that the configuration space is equivalently a space of connections;

      2. that these can be characterized by their parallel transport along paths in base space;

      3. that therefore observables of the theory are given by evaluating on choices of paths (an idea that goes by the unfortunate name “spin network”).

      All this is in Witten’s 1988 article. Of course the point there is that in the case of 3d this can actually be made to work. The reason is that in this case it is sufficient to restrict to flat connections and for these everything drastically simplifies: their parallel transport depends not on the actual paths but just on their homotopy class, rel boundary. Accordingly the “spin networks” reduce to evaluations on generators of the fundamental group, etc.

      Notice that in 4d the analog of this step that Witten easily performs in 3d was never carried out: instead, because it seemed to hard, the LQG literature always passes to a different system, where smooth connections are replaced by parallel transport that is required to be neigher smooth nor in fact continuous. These are called “generalized connections” in the LQG literature. Of course these have nothing much to do with Einstein-gravity: because there the configuration space does not contain such “generalized” fields.

      For these reasons I feel a bit uneasy when the entry refers to LQG or spin foams as “other approaches” to discuss 3d quantum gravity. First of all, the existing good discussion by Witten did realize the LQG idea already in that dimension, and it did it correctly. So in which sense are there “other approaches”?

      Which insights on 3d quantum gravity do “spin foam”s or does “group field theory”add? If anyone could list some results with concrete pointers to the literature, I’d be most grateful.

    • Changed title and links to different convention, see discussion here.

      diff, v2, current

    • added pointer to today’s

      • Adrien Brochier, David Jordan, Pavel Safronov, Noah Snyder, Invertible braided tensor categories (arXiv:2003.13812)

      diff, v8, current

    • added this pointer:

      • Christian Blanchet, Marco De Renzi, Modular Categories and TQFTs Beyond Semisimplicity (arXiv:2011.12932)

      diff, v9, current

    • gave 2d TQFT a slightly more informative Idea-section, highlighting the difference between the classical strict case classified by Frobenius algebras and the local/extended non-compact case classified by Calabi-Yau objects.

      Added a reference by Abrams as a candidate for a first rigourous proof of the classification result via Frobenius algebras, and added citations for the local case (copied over from TCFT).

    • Changed title and links to different convention, see discussion here. Also updated related concepts.

      diff, v4, current

    • changed page name to be in line with more systematic naming convention

      diff, v2, current

    • changed title to match more systematic naming convention

      diff, v14, current

    • changed page name to make it fit more systematic naming pattern

      diff, v25, current

    • Changed title and links to different convention, see discussion here. Also updated related concepts.

      diff, v3, current

    • I finally realized that this ought to exist. And sure enough, it had been constructed already: the 4d supergravity Lie 2-algebra-extension of the 4d N=2N = 2 super-Poincaré super-Lie algebra. I have added a minimum of an Idea-section and pointers to the references.

    • Changed title and links to different convention, see discussion here.

      diff, v37, current

    • summary table, to be !includeed into relevant entries, for purposes of cross-linking

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • I added the definition and several references on higher dimensional knots under knot.

    • Trivial edit to start discussion.

      What’s happening at the start here? We have both tropical rig and semiring defined. The latter is given with the extension by {∞}\{\infty\}. Is this just duplication with a mistake?

      At semiring having given 4 definitions, it says

      The nLab uses the second definition to define a semiring, and the fourth definition to define a rig. The first and third are then called nonunital semirings and nonunital rigs respectively.

      Do we really have this as a policy?

      diff, v11, current

    • Page created, but author did not leave any comments.

      v1, current

    • Added a fair bit of content to 7d Chern-Simons theory.

      Of the three examples discussed there, the first two are review. The third is inspired by something I have been talking about with D. Fiorenza, C. Rogers and H. Sati.

    • Changed title and links to different convention, see discussion here. (Unified redirects among articles about Chern-Simons theory in a particular dimension. There are now four for every artile “D=n Chern-Simons theories”, “nd Chern-Simons theory”, “nd Chern-Simons theories”, “n-dimensional Chern-Simons theory” and “n-dimensional Chern-Simons theories”.)

      diff, v3, current

    • Changed title and links to different convention, see discussion here. (Unified redirects among articles about Chern-Simons theory in a particular dimension. There are now four for every artile “D=n Chern-Simons theories”, “nd Chern-Simons theory”, “nd Chern-Simons theories”, “n-dimensional Chern-Simons theory” and “n-dimensional Chern-Simons theories”)

      diff, v6, current

    • Changed title and links to different convention, see discussion here. (Unified redirects among articles about Chern-Simons theory in a particular dimension. There are now four for every artile “D=n Chern-Simons theories”, “nd Chern-Simons theory”, “nd Chern-Simons theories”, “n-dimensional Chern-Simons theory” and “n-dimensional Chern-Simons theories”)

      diff, v7, current

    • Added to fix a dead link.

    • I made a page about the E8 lattice and its application in sphere packing

      Jurre Put

      v1, current

    • a table-for-inclusion, in order to cross-link the relevant entries

      v1, current

    • Discovering so called Magnus expansion, as an application of Lie theory to differential equations,

      • Wilhelm Magnus, On the exponential solution of differential equations for a linear operator, Commun. Pure Appl. Math. 7:4 (1954) 649–673 (1954) doi

      diff, v6, current

    • Used unicode subscripts for indices of exceptional Lie groups including title and links. When not linked, usual formulas are used. See discussion here. Links will be re-checked after all titles have been changed. (Removed two redirects for “G2-orbifold” from the top and added one for “G2-orbifold” at the bottom of the page.)

      diff, v3, current

    • giving this its own little entry, for ease of hyperlinking

      v1, current

    • I want this entry to have an actual section on construction of (compact) Examples, so I started one (here). But so far there is nothing in there apart from pointers to the original articles by Joyce and Kovalev, and a graphics illustrating Kovalev’s twisted connected sums.

      diff, v51, current

    • added to E7 the statement of the decomposition of the smallest fundamental rep under SL(8,ℝ)SL(8,\mathbb{R}) and SL(7,ℝ)SL(7,\mathbb{R}) (here) and used this then to expand the existing paragraph on As U-duality group of 4d SuGra

    • added to G2 the definition of G 2G_2 as the subgroup of GL(7)GL(7) that preserves the associative 3-form.

    • have added a minimum on the level decompositon of the first fundamental rep of E 11E_{11} here.

    • Used unicode subscripts for indices of exceptional Lie groups including title and links. When not linked, usual formulas are used. See discussion here. Links will be re-checked after all titles have been changed. (Removed two redirects for “E10” from the top and added one for “E10” at the bottom of the page.)

      diff, v11, current

    • Used unicode subscripts for indices of exceptional Lie groups including title and links. When not linked, usual formulas are used. See discussion here. Links will be re-checked after all titles have been changed. (Added redirect for “E9” at the bottom of the page.)

      diff, v7, current

    • added statement of and references for some of the homotopy groups of E 8E_8 to E8

    • expanded E6 a bit.

    • added some references on representationology of F 4F_4 to F4

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