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    • I created at equivariant cohomology separate subsections for, so far, Borel equivariant and Bredon equivariant cohomology.

      At Bredon cohomology I added a sentence about the coefficient objects.

    • The nLab entry Spectral Schemes has existed for a long time, now finally the article with that title exists, too. ;-) See the link there

    • only now realized that Zoran had an old entry moduli space of bundles. Have now vigorously cross-linked it with a bunch of related entries

    • I gave root of unity its own entry (it used to redirect to root), copied over the paragraph on properties of roots of unities in fields, and added a paragraph on the arithmetic geometry description via μ n=Spec([t](t n1))\mu_n = Spec(\mathbb{Z}[t](t^n-1)) and across-pointer with Kummer sequence.

    • I added some material on arc-connected spaces to connected space.

      I added also a reference to Willard’s General Topology, together with this online link to a Scribd document: Willard. Is this kosher (I am guessing this document is not “pirated”, but I’m not sure)?

    • Prompted by a question which I received, I went and tried to streamline the old entry Lie infinity-algebroid representation a little:

      • moved the pevious “Properties”-discussion of complexes of holomorphic bundles to the Examples-section;

      • added the example of L L_\infty-algebra extensions

      • added more information to the References-section

      • cross-linked a bit more with infinity-action and with L-infinity algebra cohomology etc.

    • I started a separate page for Picard stack (which used to be just a redirect to Picard scheme), stated the general nonsense idea with a pointer to Lurie’s thesis, where this essentially appears.

      (BWT, where in the DAG series did this end up? I forget.)

      Of course the upshot is that it’s simply the internal hom/mapping stack Pic(X)=[X,B𝔾 m]\mathbf{Pic}(X) = [X,\mathbf{B}\mathbb{G}_m]. I have a question here: it seems clear that the higher versions [X,B k𝔾 m][X, \mathbf{B}^k \mathbb{G}_m] want to be called the higher intermediate Jacobians (their deformation theory at 0 are the Artin-Mazur formal groups). Why does nobody say this? (Or if they do, where?)

    • Added stub for GAGA.
    • I have just deleted a large number of dollar \ , dollar from the bottom of Blakers-Massey theorem. The effect of such is to add a large ammount of blank space at the end of the page. Was this intentional extra space for something? If not, what is causing it? I should add that I have found similar blank space before and deleted that as well.

    • started a minimum at Calabi-Yau cohomology.

      This is an obvious idea that must have been studied before (for n2n \geq 2) but I have had no luck with finding much detail so far.

    • ;-). I found a typo ‘gorup’ and did a search on the n-Lab…. great fun! It is good to know others have disobient fingers!

    • Zoran,

      I wanted to add a reference to holomorphic Chern-Simons theory, only to realize that the entry didn't exist yet. Didn't you recently write something about holomorphic CS? I can't find it right now...

    • added references to 3d supergravity, with brief comments, and added a paragraph on how maximally supersymmetric 3d supergravity does admit an E 8(8)E_{8(8)}-gauge field (while fluxed compactification from 11d allows only proper subgroups of the global U-duality E 8(8)E_{8(8)} to be gauged)

    • wrote an entry cubical structure in M-theory.

      This reviews two stories from the literature, and points out that these two stories may be related.

      I am not sure yet exactly how much they are related. I am asking that here on PO

    • Currently, an element x in a nonassociative algebra A is nilpotent if there exist a natural number n such that x n=0x^n = 0.

      I want to say that a nilpotent left ideal of a ring R is a nilpotent element in the set of left ideals of R. To say that, I have to determine the structure of the set of left ideals of a ring under addition and multiplication. Wikipedia says that the set of ideals of a ring is a complete modular lattice. Is a complete modular lattice a nonassociative algebra? If not, do people talk about nilpotent elements in a lattice?

    • added to Mizar a quote:

      Naumowicz 06:

      One of the biggest problems that worry the developers of automated deduction systems is that their systems are not sufficiently recognized and exploited by working mathematicians. Unlike the computer algebra systems, the use of which has indeed become ubiquitous in the work of mathematicians these days, deduction systems are still seldom used. They are mostly used to formalize proofs of well-established and widely known classical theorems, the Fundamental Theorem of Algebra formalized in the systems Coq and Mizar may serve as a perfect example here. Such work, however, is not always considered to be really challenging from the viewpoint of mathematicians who are concerned with obtaining their own new results. Therefore it has been recognized as a big challenge for the deduction systems community to prove that some of the state-of-the-art systems are developed enough to cope with formalizing recent mathematics.

    • on the off-chance that there is anyone besides me who checks MathOverflow less frequently than the nnForum:

      there was a question on forcing in homotopy type theory. I took the liberty of sharing some thoughts.

      My comment reflects topics that we have discussed here at some length already. Nevertheless, when sending this I noticed that some of these discussions need to be better reflected in the nnLab. And in particular better than I have commented on them for the moment.

      I won’t further look into this right now as I am busy with something else. But later I’d like to come back to this.

    • Let us define a (co-)homology XX-cobordism, where XX is a path connected space with basepoint **:

      Definition: A (co-)homology XX cobordism M:Λ 0Λ 1M:\Lambda_0\to\Lambda_1 is a cobordism MM such that H (M)=H (X)H^\bullet(M)=H^\bullet(X) for cohomology and H (M)=H (X)H_\bullet(M)=H_\bullet(X) for homology, where H (A)= k dimAH k(A)H^\bullet(A)=\bigoplus^{\dim A}_{k\in\mathbb{N}}H^k(A) and H (A)= k dimAH k(A)H_\bullet(A)=\bigoplus^{\dim A}_{k\in\mathbb{N}}H_k(A).

      Definition: A 𝒞\mathcal{C} valued (co-)homology QFT is a symmetric monoidal functor (Co)HomCob(n,X)𝒞(Co)HomCob(n,X)\to\mathcal{C}, where the morphisms in (Co)HomCob(n,X)(Co)HomCob(n,X) are (co-)homologyXX-isomorphisms of (co-)homology XX-cobordisms, defined as an isomorphism Φ:MM \Phi:M\to M^\prime such that Φ( +M)=M + \Phi(\partial_+ M)=M^\prime_+ and Φ( M)=M \Phi(\partial_- M)=M^\prime_-.

      What could possible uses of such a QFT be? Can this be related to Homotopy QFTs by the Hurewicz homomorphism π k(M)H k(M)\pi_k(M)\to H_k(M)?

    • I created a stub at Long March as someone had started an empty entry there. For the moment it directs back to Galois theory where there is mention of the discussion at Long March, doh! I should prepare a longer entry, but do not understand the topic that well.

    • Wrote continued fraction, emphasizing coalgebraic aspects. More links should be inserted, and some more material needs to be filled in.

    • There seem to be some misleading remarks at Čech model structure on simplicial presheaves.

      Accordingly, the (∞,1)-topos presented by the Čech model structure has as its cohomology theory Čech cohomology.

      Marc Hoyois seems to says the opposite: there is no deep relation between “Čech” in “Čech cohomology” and in “Čech model structure”.

      […] the corresponding Čech cover morphism .

      Notice that by the discussion at model structure on simplicial presheaves - fibrant and cofibrant objects this is a morphism between cofibrant objects.

      The Čech nerve is projective-cofibrant if we assume the site has pullbacks. I don’t know how to prove it otherwise. Of course, injective-cofibrancy is trivial.

      this question is evidently also relevant to what the correct notion of internal ∞-groupoid may be

      Based on the discussion here, it seems that the Čech model structure is not site-independent, even though it can be defined on the category of simplicial sheaves. A very strange state of affairs…