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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeJul 12th 2012

I have expanded the Idea-section at deformation quantization a little, and moved parts of the previous material there to the Properties-section.

• CommentRowNumber2.
• CommentTimeJan 8th 2013
• (edited Jan 8th 2013)

I just added some rough notes from a lecture John Jones gave this morning (http://www.newton.ac.uk/programmes/GDO/gdow01). I didn't manage to get all the TeX right the first time, and the nLab seems down now so I will have to fix it later.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeJan 8th 2013

Thanks!! That’s great.

I’ll maybe go through it in a few minutes to fix the instiki-syntax errors (I guess you were copy-and pasting? )

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeJan 9th 2013

Ah, I see you are editing right now. I was just about to look into it.

(It’s strange that the link to HKR theorem does not work. (?))

• CommentRowNumber5.
• CommentTimeJan 9th 2013

I am just not used to the instiki TeX so I usually have to do my best and then keep editing the page until I have fixed everything. For the HKR theorem, I fixed it by making "Theorem" lowercase.

I will add some remarks on the Deligne conjecture that Jones also made (which I was too tired to type yesterday).

• CommentRowNumber6.
• CommentTimeJan 9th 2013

Done, also added a page for John Jones.

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeJan 9th 2013

Thanks!

• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeJan 25th 2013

I am beginning to expand deformation quantization to include the discussion of deformation quantization of field theories by Costello-Gwilliam. So far I began to restructure the Definition-section accordingly. Will now fill in material, as time permits.

But meanwhile: in the course of this I slightly rearranged the material whose addition was announced in #5, #6 above. For instance the definition of Poisson manifolds and their deformation I moved out of the Properties-section into the Definition-section. This now makes Kontsevich’s theorem sit a bit lonely in a single subsection in the Properties-section. But I guess eventually we should expand there on its proof, which will justify a dedicated subsection after all.

I am thinking the relation discussed further below to Hochschild and cyclic cohomology deserves to be highlighted and expanded on much more, eventually. I’ll see what I can do. Will be forced offline in a short while, though.

• CommentRowNumber9.
• CommentAuthorUrs
• CommentTimeApr 23rd 2013
• (edited Apr 23rd 2013)

I slightly re-arranged the references at deformation quantization. Igor Khavkine rightly amplified to me that Fedosov’s deformation quantization already applies also to (regular) Poisson manifolds, which was not well-reflected in the entry. So I moved that to the top of the list, where it seems to belong, so that Kontsevich’s result is now a little bit below.

• CommentRowNumber10.
• CommentAuthorUrs
• CommentTimeJun 12th 2013
• (edited Jun 12th 2013)

Added the following quote from section 1.4

to the Idea-section at deformation quantization (with a tad of commentary):

Generally speaking, physics is based on $[$ strict $]$ quantization, rather than $[$ formal $]$ deformation quantization, although conventional quantization sometimes leads to problems that can be treated by deformation quantization.

• CommentRowNumber11.
• CommentAuthorUrs
• CommentTimeAug 19th 2013
• (edited Aug 19th 2013)

added to the section Motivic Galois group action on the space of quantizations a pointer to the proof by Dolgushev that $\pi_0$ of the space of formal deformation quantizations of an $\mathbb{R}^n$ is indeed (a torsor over) the Grothendieck-Teichmüller group.

(Just heard a talk about this at GAP XI. Therefore just a brief pointer, don’t have much time)

• CommentRowNumber12.
• CommentAuthorUrs
• CommentTimeAug 20th 2013