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1. I’ve started writing the notes of the talk I’ll be giving in Utrecht next week. They are here

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeMar 2nd 2011

nice. Would you mind if I made some trivial edits to the page? I have the urge to make a bunch of keywords hyperlinked ;-)

For some the relevant $n$Lab pages do not exist yet. It would be nice to create a stub for Artin algebra, for instance.

2. Hi Urs, I absolutely don’t mind. And I’ll keep creating stubs for missing nLab pages when you link them from my notes :)

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeMar 2nd 2011
• (edited Mar 2nd 2011)

Apart from Artin algebra there are now some unsatisfied links to very basic concepts such as complex manifold and holomorphic function which unfortunately we still do not have nLab entries about. Don’t feel pressured by these. But maybe you’d enjoy creating quick stub etries for these with just a 1-line Idea and maybe one standard reference.

(Myself, I am on the train right now and won’t be able to do much more at the moment.)

3. I’ve now created Artin ring and descending chain condition. now I’ll go on with the notes before creating new stubs.

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeMar 2nd 2011

created a stub for complex manifold and holomorphic function. Just so that these links don’t appear greyish.

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeMar 2nd 2011
• (edited Mar 2nd 2011)

thanks for Arting ring

I have linked it back and forth with infinitesimally thickened point. Maybe cross-check if you agree about my use of terminology there.

4. added a section on Cartan homotopies. while converting it from an old latex source of mine I thought “hey, but this is what I now would call the inner derivation Lie 2-algebra!” and indeed Cartan calculus was there :)

• CommentRowNumber9.
• CommentAuthorTim_Porter
• CommentTimeMar 3rd 2011

Some accents were coming out strangely in the title of Cartan’s work. I fixed them but please check that my fix works on your machines!

• CommentRowNumber10.
• CommentAuthorUrs
• CommentTimeMar 3rd 2011

added a section on Cartan homotopies.

It’s looking good. When you are close to being finished, should I post a pointer to these notes to the announcement blog post here? I think it would be a nice advertizement both of your talk and of the usefulness of having $n$Lab notes :-)

while converting it from an old latex source of mine I thought “hey, but this is what I now would call the inner derivation Lie 2-algebra!” and indeed Cartan calculus was there :)

Okay, good. I had created that entry being pushed by Jim, who kept saying we should emphasize more manifestly how Cartan calculus sits inside $\infty$-Lie theory.

I keep meaning to write also an entry on how all things called “derived brackets” is similarly just a way to talk about the full automorphism infinity-Lie algebra.

But not right now, I need to urgenty be doing something else now.

5. It’s looking good. When you are close to being finished, should I post a pointer to these notes to the announcement blog post here? I think it would be a nice advertizement both of your talk and of the usefulness of having nLab notes :-)

Sure: that’s precisely the reason why I’m writing the notes in advance :)

I’ll post here when I’ll be almost finished.

6. the current status of the notes is:

Newlander-Nierenberg approach: to be completed

Kodaira-Spencer approach: to be written

The Deligne groupoid: to be completed

Gauge vs. homotopy equivalent Maurer-Cartan elements: to be written

Back to classical deformations: to be written

Other sections are complete. Note ready for blog post announcement, yet, but at least now they are readable.

• CommentRowNumber13.
• CommentAuthorUrs
• CommentTimeMar 3rd 2011

Note ready for blog post announcement, yet, but at least now they are readable.

Okay, by the way, you can maybe just post the announcement yourself when you are ready: just post a comment to the thread that I had started on the $n$Cafe.

7. sure that’s the best way. I also just noticed in terror that a typo can change “not” in “note” and “note ready for blog post announcement” could have had terrific consequences.. :)

• CommentRowNumber15.
• CommentAuthorUrs
• CommentTimeMar 3rd 2011

a typo can change “not” in “note”

the “yet” saved you (and only that ;-)

• CommentRowNumber16.
• CommentAuthorjim_stasheff
• CommentTimeMar 5th 2011
Urs wrote:
I keep meaning to write also an entry on how all things called "derived brackets" is similarly just a way to talk about the full automorphism infinity-Lie algebra.

Technically that maybe ok, but it's like saying poetry is just a way to write prose
8. Note ready for blog post announcement :)

(I’m taking care of that)

• CommentRowNumber18.
• CommentAuthorUrs
• CommentTimeMar 7th 2011

Thanks, Domenico! Would it make sense to insert at the beginning the abstract of your talk? Or some other kind of summary or intro?

9. Hi Urs,

I hadn’t thought of that, but it is indeed a good idea to have there at the beginning the abstract and a link to the workshop web page. I’m now adding these data.

• CommentRowNumber20.
• CommentAuthorUrs
• CommentTimeMar 7th 2011
• (edited Mar 7th 2011)

Hi Domenico,

one minor-minor typo: in the displayed equation above the line that starts with “where the bracket is the graded commutator” one backslash is missing in the source code!

10. Hi Urs,

thanks for having spotted that. there was also an \overline missing, now I’ve corrected that. please, feel free to edit the notes text.

• CommentRowNumber22.
• CommentAuthorzskoda
• CommentTimeMar 7th 2011
• (edited Mar 7th 2011)
Domenico, I find it very useful when the arxiv number is not hidden from the reference list; I mean if the link is already provided it is good to be in the title of the link. E.g. I often know the author and recall the year of the paper but do not recognize which paper it is by title. When offline or looking at printed version I can not figure that out (and even then it is inconvenient to read the page needing to scroll cursor to every reference to highlight, and on some browsers the link does not highlight, unless one calls the page). So I find that the format [arxiv:0999999], or a variant, is better than [arxiv] only. For doi this is not so, as nobody finds useful doi number so it is better to hide the doi number into the link.
• CommentRowNumber23.
• CommentAuthorzskoda
• CommentTimeMar 8th 2011
I have added some references to Deligne groupoid, calculus of variations and related entries. Getzler has Deligne's 1994 letter to Deligne but he says it should not be linked to without permission. These ideas are also in a related paper of Getzler which is leading to normal forms which are superimposable to certain Hamiltonians of Dubrovin and Novikov. I linked Hinich's papers as well. Hinich more recently wrote a note on the homotopy coherent nerve, where he also explains/corrects his earlier 3 papers in deformation theory which are correct except for the point that in some constructions he should have in fact used homotopy coherent nerve.
• CommentRowNumber24.
• CommentAuthorUrs
• CommentTimeMar 8th 2011

I have added some references to Deligne groupoid, calculus of variations and related entries.

Thanks! That’s useful.

• CommentRowNumber25.
• CommentAuthorTim_Porter
• CommentTimeMar 8th 2011
• (edited Mar 8th 2011)

Hinich’s use of the h.c. nerve suggests to me that his version of Deformation Theory should be possibly nearer to the n-POV than was thought of when he wrote the first few papers on that approach.