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brief category:people-entry for hyperlinking references at Sasakian geometry
added some text to the beginning of the category:people entry Michael Hopkins. Currently it reads as follows:
Michael Hopkins is a mathematician at Harvard University.
Hopkins is a world leading researcher in algebraic topology and (stable-)homotopy theory.
Among his notable achievements are his work on the Ravenel conjectures, the introduction and discussion of the generalized cohomology theory tmf and its string orientation, a formalization and construction of differential cohomology, the proof of the Kervaire invariant problem. More recently via Jacob Lurie’s work on the cobordism hypothesis Hopkins participates in work related to the foundations of quantum field theory.
I have added to homotopy coherent diagram and to model structure on algebras over an operad the fact that one can describe homotopy coherent diagrams as algebras over the Boardman-Vogt resolution of some operad. Vogt’s rectification theorem is then a special case of the general Berger-Moerdijk result.
In the course of this I reorganized and expanded homtopy coherent diagram a bit. It still needs to be polished a bit.
brief entry nilpotence theorem
(in chromatic homotopy theory, maybe needs disambiguation later…)
I have touched the following entries, trying to interlink them more closely by added sentences with cross-links that indicate how they relate to each other:
Also linked for instance to semicategory from category, etc.
Linked also to Delta space, but the entry doe not exist yet.
starting a stub, for the moment just to record references.
There is a plethora of constructions in the literature. Has anyone discussed in detail if/how these relate to the evident general abstract definition (maps of -stacks from the given geometric groupoid to the Deligne complex)?
I see that some authors, like Redden, partially go in this direction, but I haven’t seen yet a comprehensive account to this extent.
Created reflective factorization system.
at KLT relations I have expanded the list of references. I added also references for the generalization of these relations that is known these days as “gravity is Yang-Mills squared” or similar (eventually this might want to be a separate entry).
In this course I also expanded the list of references at quantum gravity – As a perturbative quantum field theory
I found the definition of a scheme to be slightly unclear/insufficiently precise at one point, so I have tweaked things slightly, and added more details. Indeed, it is quite common to find a formulation similar to ’every point has an open neighbourhood isomorphic to an affine scheme’, whereas I think it important to be clear that one does not have the freedom to choose the sheaf of rings on the local neighbourhood, it must be the restriction of the structure sheaf on .
edited at orbispace in order to express Charles Rezk’s statement here more accurately.
brief category:people-entry for hyperlinking references at supergeometry supermanifolds, super Lie groups, functorial geometry
brief category:people-entry for hyperlinking references at supergeometry supermanifolds, super Lie groups, functorial geometry
I have added a little bit to supermanifold, mainly the definition as manifolds over superpoints, the statement of the equivalence to the locally-ringed-space definition and references.
Added the Yoneda-embedding way to talk about group objects and hence supergroups.
am starting an entry contact manifold
added pointer to
brief category:people-entry for hyperlinking references at embedding of smooth manifolds into formal duals of R-algebras
I finally gave this statement its own entry, in order to be able to conveniently point to it:
embedding of smooth manifolds into formal duals of R-algebras
I have been indexing Kochman’s excellent book Bordism, Stable Homotopy and Adams Spectral Sequences and in the course I have touched all the relevant entries
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 ?
brief category:people-entry for hyperlinking references at G-structure
I am finally splitting this off from G-structure. Have added comments on the disambiguation both here and there
brief category:people-entry for hyperlinking references at factorization homology and orbifold