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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• I added a comment on the Calabi-Yau variety page about $c_1=0$. Does anyone know if it’s still true in the non-compact case?

Also, what’s the proper way to add questions/parenthetical remarks to n-Lab pages?

• started TCFT

eventually we should better reflect at the relevant nLab entries that Costello’s classification result of 2d TCFTs – proving the corresponding conjecture by Kontsevich – was the precurser of the proof of the full cobordism hypothesis: Hopkins and Lurie tried to generalize Costello’s proof (they had not actually heard of Baez-Dolan back then).

• Just got the following query from Harald Hanche-Olsen about the page separation axioms. As I’ve never seen that notation before either (but agree with Harald’s comments in both parts), I’m forwarding it here so that the person who first adopted it (Toby?) or others can chip in.

I hadn’t seen the notation $\stackrel\circ\ni$ for a neighbourhood before, but it looks like a reasonable notation that I might want to adapt. BUT it seems more appropriate for a neighbourhood of a point rather than a neighbourhood of a set. Wouldn’t $\stackrel\circ\supset$ or $\stackrel\circ\supseteq$ be more appropriate for that case? What is the rationale for the usage on that page?

• edited the entry orthogonality a bit, for instance indicated that there are other meanings of orthogonality. This should really be a disambiguation page.

And what makes the category-theoretic notion of orthogonality not be merged with weak factorization system? And why is orthogonal factorization system the first example at orthogonality if in fact that imposes unique lifts, while in orthogonality only existence of lifts is required?

I think the entry-situation here deserves to be further harmonized.

• created stub for Pfaffian line bundle, because I needed the link to the entry and to the single reference currently given there. Will fill in more details later today.

In the course of this I also created an extremely stubby entry fermion.

• Over at orthogonal subcategory problem, it’s not clear to me whether or not the “objects orthogonal to $\Sigma$” should be morphisms orthogonal to $\Sigma$, or if it should mean objects of $X$ of $C$ such that $X\to *$ is orthogonal to $\Sigma$ (where $*$ denotes the terminal object). (Hell, it could even mean objects that are the source of a map orthogonal to $\Sigma$). I was in the process of changing stuff to fit the first interpretation, but I rolled it back and decided to ask here.

If it should in fact be the second (or third) definition, I would definitely suggest changing the notation $\Sigma^\perp$, which is extremely misleading, since that is the standard notation for the first notion.

• added to Lie infinity-groupoid a section on Circle Lie n-groupoids, i.e. those of the form $\mathbf{B}^n U(1)$, and their relation to Cech- , Deligne-, and de Rham cohomology.

• since it was demanded at the “counterexamples”-page, I created 3-manifold. This made me create Poincare conjecture.

I find it striking that Hamilton’s Ricci flow program and Perelman’s proof by adding the dilaton hasn’t found more resonance in the String theory community. After all, this shows a deep fact about the renormalization group flow of non-critical strings on 3-dimensional targets with gravity and dilaton background.

I once chatted with Huisken and indicated that this suggests that there is a more general interesting mathematical problem where also the Kalb-Ramond field background is taken into account. I remember him being interested, but haven’t heard that anyone in this area has extended Perelman’s method to the full massles string background content. Has anyone?

• counterexamples in algebra inspired (and largely copied from) this MO question since MO is a daft place to put that stuff and a page on the nLab seems better. (A properly indexed database would be even better, but I don’t feel like setting such up and don’t know of the existence of such a system)

• Cleaned up Bell’s theorem a bit in my ongoing effort to better organize and clean up the quantum mechanics entries.

• As a small step towards more information about representations of operator algebras and their physical interpretation in AQFT, I extraced states from operator algebras and added Fell’s theorem. This is a theorem that is often cited in the literature, but most times not with any specific name (often with no reference, either). But I think it is both justified and usefule to call it Fell’s theorem :-)

• I am trying to remove the erroneous shifts in degree by $\pm 1$ that inevitably I have been making at simplicial skeleton and maybe at truncated.

So a Kan complex is the nerve of an $n$-groupoid iff it is $(n+1)$-coskeletal, I hope ;-)

At truncated in the examples-section i want to be claiming that the truncation adjunction in a general (oo,1)-topos is in the case of $\infty$Grpd the $(tr_{n+1} \dashv cosk_{n+1})$-adjunction on Kan complexes. But I should be saying this better.

• The mass of a physical system is its intrinsic energy.

I expect that Zoran will object to some of what I have written there (if not already to my one-sentence definition above), but since I cannot predict how, I look forward to his comments.

• John Baez has erased our query complaining about disgusting picture at quasigroup, and left the picture. I like the theory of quasigroups but do not like to visit and contribute to sites dominated by strange will to decorate with self-proclaimed humour which is in fact tasteless.

• added to CartSp a section that lists lots of notions of (generalized) geometry modeled on this category.

• added more details to the definition of the homotopy sheaves;

• added a section on how the Joyal-Jardine homotopy sheaves of simplicial presheaves are a model for that.

• continued from here

my proposal:

Connes fusion is used to define fusion of positive energy representations of the loop group $\mathcal{L}SU(N)$ in * Antony Wassermann, Operator algebras and conformal field theory III (arXiv) and to define elliptic cohomology in * Stephan Stolz and Peter Teichner, What is an elliptic object? (link)

and removing the query box.