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• brief category:people-entry for hyperlinking references at Sasakian geometry

• Added redirects and a description of other contributions.

• Stub with references.

• I have fixed the URL of my webpage

Philippe Gaucher

• 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 $\infty$-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.

• I agree – corrected point 3 having checked Carboni-Lack-Walters

• 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 gravityAs 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 $X$.

• edited at orbispace in order to express Charles Rezk’s statement here more accurately.

• 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.

• I thought we had a reference for this on the $n$Lab, but now I don’t find it:
What’s a citation for the statement that $\infty Groupoids$ is the terminal object in $(\infty,1)Toposes$?
• I do not understand the entry G-structure. G-structure is, as usual, defined there as the principal $G$-subbundle of the frame bundle which is a $GL(n)$-principal bundle. I guess this makes sense for equivariant injections along any Lie group homomorphism $G\to GL(n)$. The entry says something about spin structure, warning that the group $Spin(n)$ is not a subgroup of $GL(n)$. 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) $Spin(n)$-bundle by pulling back along a fixed noninjective map $Spin(n)\to GL(n)$ 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