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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
Wrote superextensive site, with a purported proof that sheafification for the single covers does preserve extensive-sheaves in that case.
Have started some minimum at calibration.
Zoran just wrote Hurewicz fibration.
have started a category:reference entry on
and have added pointers to it from relevant entries
I added redirets Atiyah sequence, Atiyah class, Atiyah algebroid to Atiyah Lie algebroid. Maybe we want to have Lie algebroid aspect (concentrating on bracket) and the cohomological/derived category aspect (cohomology class of the exact sequence of modules) separate in fuiture, but now the material is still too small. I added a number of interesting references and a sentence on the class.
created celestial sphere
added a few items to the References section at GUT, both on theoretical background as well as on fits to the latest experimental data. According to these, the SO(10)-model seems to be well alive, susy or not.
I have created a new entry
meant as a disambiguation page for the various different kinds of definitions that exists. Presently it points to the entries
that already provide dedicated discussion of special defintiions. In addtion it lists references that have further proposals for defintion which don’t at the moment however have dedicated nLab pages associated with them.
Wrote cumulative hierarchy, and edited some at ZFC (idea section, reference, related articles).
started stub for higher parallel transport (but no definition yet, just examples and pointers)
I just noticed we miss an entry n-vector space. I’d like to start it, but I only have a very vague idea, recursively implementing the notion of Baez-Crans 2-vector space. something like: an n-vector space is an (n−1)-category of modules over a (n−1)-Vect enriched symmetric monoidal (n−1)-category.
how far is this from the correct notion?
I was going to add a stub page on Roland Schwänzl, to avoid grey links, and linking to the Wikipedia page, but looking at that I am very confused (and my German is too rusty!) That page seems to be about two people or did Roland Schwänzl actually do things on UNIX etc as well as working with Vogt? My search did not even give me the genealogy page for him, (although I now have found it).. Can anyone help?
The nLab presently gives me an application error when trying to open anything, so I’ll record some things here.
The following needs to be added to the References-section of the entry M-theory super Lie algebra:
The M-theory super Lie algebra as first considered in
Jan-Willem van Holten, Antoine Van Proeyen, N=1 supersymmetry algebras in d=2,3,4mod8 J.Phys. A15, 3763 (1982).
Paul Townsend, p-Brane Democracy (arXiv:hep-th/9507048)
Discussion of its formulation in terms of octonions (see also at division algebra and supersymmetry) includes
- A. Anastasiou, L. Borsten, Michael Duff, L. J. Hughes, S. Nagy, An octonionic formulation of the M-theory algebra (arXiv:1402.4649)
I fixed a link that was not working. (The brackets were interfering with the link address.) see here
I created Hoàng Xuân Sính as a result of recent G+ discussion, and David Eppstein creating an English Wikipedia page for her. There is now a link to that page at 2-group and a(n updated) link to her thesis.
for those who check the logs and are wondering: I went through a fairly long list of category:people-entries on people based in and around London, updating affiliation links, references and related nLab entries.
discovered that we already had a stub on Weyl quantization. Cross-linked a bit and added the following reference on Weyl quantization of Chern-Simons theory (also to quantization of 3d Chern-Simons theory):
Jørgen Andersen, Deformation quantization and geometric quantization of abelian moduli spaces, Commun. Math. Phys., 255 (2005), 727–745
Razvan Gelca, Alejandro Uribe, The Weyl quantization and the quantum group quantization of the moduli space of flat SU(2)-connections on the torus are the same, Commun.Math.Phys. 233 (2003) 493-512 (arXiv:math-ph/0201059)
Razvan Gelca, Alejandro Uribe, From classical theta functions to topological quantum field theory (arXiv:1006.3252, slides pdf)
Razvan Gelca, Alejandro Uribe, Quantum mechanics and non-abelian theta functions for the gauge group SU(2) (arXiv:1007.2010)
I have added a new link to the page on Grothendieck. There is a good new article on a CNRS site.
given the concept of Heisenberg Lie n-algebra, there is an evident definition of Weyl n-algebra: its universal enveloping E-n algebra.
I noted that down for reference at Weyl n-algebra. In the process I noticed that Markarian proposed a different definition just a few months back
Just some obvious stuff at maximal partial function to satisfy some links.
started a stub for moduli space of Calabi-Yau spaces. Nothing really there yet, except some references and some cross-links.
I tried to start an entry theta function, but it’s hard to tell for me if anything of it has been saved. The nLab is too busy doing something else than serving pages.
I have added the statement of lemmas 4.1, 4.2 of Menni-Lawvere to cohesive topos here and to points-to-pieces transform here.
I am starting a table of contents theta functions - contents and am including it as a “floating table of contents” into relevant entries
The entry entitled (x, y) ⊙ (u, v) = (xu + 2yv, xv + yu) has been started. Is it Spam? or does that definition mean something useful to the nPOV.
made explicit in the Idea section of functional equation the statement that the functional equation of a zeta function is the incarnation under Mellin transform of the automorphy of the automorphic form that it comes from
gave automorphic L-function a minimum of an Idea-section, presently it reads as follows:
An automorphic L-function Lπ is an L-function built from an automorphic representation π, in nonabelian generalization of how a Dirichlet L-function Lχ is associated to a Dirichlet character χ (which is an automorphic form on the (abelian) idele group).
In analogy to how Artin reciprocity implies that to every 1-dimensional Galois representation σ there is a Dirichlet character χ such that the Artin L-function Lσ equals the Dirichlet L-function Lχ, so the conjectured Langlands correspondence says that to every n-dimensional Galois representation σ there is an automorphic representation π such that the automorphic L-function Lπ equals the Artin L-function Lσ.
stub for holomorphic block, for the moment just to record two references
gave prequantum line bundle a little entry of its own
Wrote Engeler’s lemma, something I hadn’t heard of until recently.
I added a few comments to Hilbert basis theorem about related work by Gordon and Noether (chronologically, on either side of Hilbert’s work).
I created the article left-determined model category.
I had begun adding to prime ideal theorem (en route adding to compactness theorem), but have decided to stop midstream because it looks as though much more general results are known, which I’d need to read up on it before writing further.
One thing I’ll mention now is that the surmise (due to Toby?) that UF is equivalent to the prime ideal theorem for rigs seems to be known and subsumed under these general results. Banaschewski’s name comes up as one having a key lattice-theoretic insight into this topic: “Every nontrivial distributive complete lattice with a compact top element contains a prime element.”
The entry finite field was looking a little sad, so I added to it.
Created splitting field.
Do we have a page about natural transformations between (∞,1)-categories? I wanted to add a link to this paper (working today on catching up with the arXiv…) but I couldn’t find where to put it.
New entry binormal topological space.
We have a bit of a mess of closely related entries related to étale homotopy groups which existed more or less in parallel without seeming to know much of each other. I have tried to do some minimum of cross-linking and cleaning up, but this needs more attention.
There is more even, there is Grothendieck’s Galois theory and what not. (Maybe we need to wait until somebody gives a course on this and uses the occasion to clean it all up and harmonize it.)
Created exponent of a group.
I added more material to unique factorization domain.
I’ve slowly been trying to improve the article topological map since this thread. I just added a small note on embedded graphs versus abstract graphs, motivated by Bruce Bartlett’s interesting recent post at the n-café.
I created a stub for falling factorial, mainly to record the simple fact I learned yesterday that it counts the number of injections between two finite sets.
There doesn’t seem to be a discussion for this page differential cohesion and idelic structure. Is this to be the general page for ’inter-geometry’?
If so, it might be worth recording An Huang, On S-duality and Gauss reciprocity law, (Arxiv).
added to eta invariant a lightning section On manifolds with boundaries: as sections of the determinant line, essentially just a glorified pointer to Freed 95 for the time being.
Created intermediate model structure. Needs more cross-linking, but I have to go.
In two recent threads [1, 2] I had started to look into elementary formalization of the following obstruction problem in higher geometry:
given
a Klein geometry H→G,
a WZW term LWZW:G/H⟶Bp+1𝔾conn;
a Cartan geometry X modeled on G/H
then:
Here are first concrete observations, holding in any elementary ∞-topos (meaning: this may be proven using HoTT, not needing simplicial or other infinite diagrams):
First, a lemma that turns the datum of a global WZW term Fr(X)⟶Bp+1𝔾conn on the frame bundle of X (each of whose fibers looks like the formal disk 𝔻 around the base point, or any other point, in G/H) into something closer to cohomological data on X. In the following Fr(X) may be any fiber bundle E and Bp+1𝔾conn may be any coefficient object A.
Lemma. Let E→X be an F-fiber bundle associated to an Aut(F)-principal bundle P→X. Then A-valued functions on E are equivalent to sections of the [F,A]-fiber bundle canonically associated to P.
Proof. By the discussion at infinity-action, the universal [F,A]-fiber bundle [F,A]/Aut(F)→BAut(F) is simply the function space [F,A]BAut(F) formed in the slice over BAut(F), with F regarded with its canonical Aut(F)-action and A regarded with the trivial Aut(F)-action.
Now, by universality, sections of P×Aut(F)[F,A]→X are equivalently diagonal maps in
[F,A]/Aut(F)↗↓X⟶BAut(F)But by Cartesian closure in the slice and using the above, these are equivalent to horizontal maps in
E=P×Aut(F)F⟶A×BAut(F)↘↙BAut(F)Finally by (∑BAut(F)⊣BAut(F)*) this is equivalent to maps E→A. □
[ continued in next comment ]
am splitting off complex volume from hyperbolic manifold
stub for Bloch group
added details to Borel regulator, with discussion of Becker-Gottlieb transfer and the refinement to differential algebraic K-theory by the transfer index conjecture.
started some minimum at odd Chern character and cross-linked a little
I created Michal-Bastiani smooth map, and linked to it from diffeological space, Andree Ehresmann and locally convex topological vector space.
Very stubby beginning of BHK interpretation.
Started Witt-Burnside functor.
I split off coprojection from projection and added a remark about their monicity (or lack thereof).
I added a new section to Bayesian reasoning, Exchangeability, which outlines the de Finetti Representation theorem. As indicated, there’s a multivariate version. This was used to talk about Bose-Einstein statistics.
I wonder if anything interesting would happen with a HoTT rendition of statistical meachanics.
Someone has got the Euler-Lagrange equation page to redirect to hollymolly, and added that word at the bottom. How do we undo such vandalism?
during a talk on homotheties of Cartan geometries that I heard yersterday, it occurred to me that this concept has an immediate simple general abstract formulation in differential cohesive homotopy theory. Made a note on this now at homothety.