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brief category:people-entry for hyperlinking references at Dp-D(p+2)-brane bound states, Yang-Mills monopoles, knot invariants, chord diagrams and fuzzy spheres.
a minimum, to give a home to
on D1-D7 brane intersections as fuzzy funnels on fuzzy 6-spheres
brief category:people-entry for hyperlinking references at fuzzy funnel, D1-D3 brane intersection, D1-D5 brane intersection
brief category:people-entry for hyperlinking references at generalized complex geometry and G-structure
I do not understand the entry G-structure. G-structure is, as usual, defined there as the principal -subbundle of the frame bundle which is a -principal bundle. I guess this makes sense for equivariant injections along any Lie group homomorphism . The entry says something about spin structure, warning that the group is not a subgroup of . So what is meant ? The total space of a subbundle is a subspace at least. Does this mean that I consider the frame bundle first as a (non-principal) -bundle by pulling back along a fixed noninjective map and then I restrict to a chosen subspace on which the induced action of Spin group is principal ?
I am working on entries related to generalized complex geometry. My aim is to tell the story in the correct way as the theory of the Lie 2-algebroid called the
Most, if not all, of the generalized complex geometry literature, uses the "naive" definition of Courant algebroids that regards them as vector bundles with some structure on them and is being vague to ignorant about what the right morphisms should be.
As discussed at Courant algebroid we know that we are really dealing with a Lie 2-algebroid and hence know where precisely this object lives. This provides some useful, I think, perspectives on some of the standard constructions. I want to eventually describe this. For the moment I have just the material at standard Courant algebroid with only two most basic observations (which, however, in my experience already take a nontrivial amount of time on the blackboard to explain to somebody used to the "naive" picture usually presented in the literature).
brief category:people-entry for hyperlinking references at G-structure and at holographic QCD
(if anyone has a webpage for this author, let’s add the URL)
stub for special holonomy, just to record two references for the moment.
Also added a line to the Idea-section at holonomy that mentions holonomy group and special holonomy.
I have added to cotensor product a section, here, with some basics on cotensor products of comodules over commutative Hopf algebroids. The same stuff I have added also in the respective section at commutative Hopf algebroid
Created Ho(Cat), mainly as a place to put a counterexample showing that it doesn't have pullbacks. If anyone has a simpler one, please contribute it.
I added to duality in physics a reference to a form of mirror symmetry being a derived Morita equivalence. So also created a stub for derived Morita equivalence.
This is intended to continue the issues discussed in the Lafforgue thread!
I have added an idea section to Morita equivalence where I sketch what I perceive to be the overarching pattern stressing in particular the two completion processes involved. I worked with ’hyphens’ there but judging from a look in Street’s quantum group book the pattern can be spelled out exactly at a bicategorical level.
I might occasionally add further material on the Morita theory for algebraic theories where especially the book by Adamek-Rosicky-Vitale (pdf-draft) contains a general 2-categorical theorem for algebraic theories.
Another thing that always intrigued me is the connection with shape theory where there is a result from Betti that the endomorphism module involved in ring Morita theory occurs as the shape category of a ring morphism in the sense of Bourn-Cordier. Another thing worth mentioning on the page is that the Cauchy completion of a ring in the enriched sense is actually its cat of modules (this is in Borceux-Dejean) - this brings out the parallel between Morita for cats and rings.
Morita context in works!
some trivial edits to opetope (a toc, some hyperlinks)
added pointer to today’s
collected some references on the interpretation of the !-modality as the Fock space construction at !-modality.
Cross-linked briefly with he stub entries_Fock space_ and second quantization.
felt the need to split off a separate entry for circle n-group
I have split off from holographic principle and then expanded a good bit a few paragraphs on
AdS3-CFT2 and CS-WZW correspondence
together with a few commented references, trying to amplify how this case is given by an actual well-known theorem and at the same time seems to be generic for the more general cases of AdS-CFT which are currently much more vague.
brief category:people-entry for hyperlinking references at G-structure, M-theory on Spin(7)-manifolds, Landau-Ginzburg model, D=5 supergravity
earlier today I had created a stub for anti de Sitter spacetime
started cubical type theory using a comment by Jonathan Sterling