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September 6, 2008

Waldorf on Transport Functors and Connections on Gerbes

Posted by Urs Schreiber

Konrad Waldorf used to be a PhD student in Hamburg until recently and has now moved to Berkeley. Upon arrival there he has now given two talks on our joint work on parallel 2-transport. You can find nicely readable slides of his talks on his website

Konrad Waldorf
Connections on non-abelian gerbes and their holonomy
(pdf slides part I, part II)

As nn-Café-regulars know, this is based on our series of joint articles

U. S., K. W.
Parallel transport and functors
(blog, arXiv)
Smooth 2-functors and differential forms
(blog, arXiv)
Connections on nonabelian gerbes and their holonomy
(blog, arXiv)

which in turn goes back to my joint work with John Baez

J. B. , U.S.
Higher gauge theory
(blog, arXiv)

and my thesis (blog, arXiv), where the diagrams for 2-holonomy first appeared, which we now identified as cells in the codescent 2-groupoid (the 2-groupoid of “2-paths in the Čech 2-groupoid”) and describe in precise detail. I had already talked about the basic idea in Vietri 05, where I also met Roger Picken whose work

M. Mackaay, R. Picken
Holonomy and parallel transport for abelian gerbes
(arXiv)

was very influential for the development of Higher gauge theory (John Baez’s review page) aka nonabelian differential cohomology (lecture notes).

Just recently Roger Picken with João Martins followed up on this in the non-abelian context

J. Martins, R. Picken
On two-dimensional holonomy
(arXiv)
Cubical 2-bundles with connection and Wilson spheres
(arXiv)

They use the cubical model for 2-groupoids where we use the globular one, but our two discussions of nonabelian differential cocycles are otherwise pretty close.

Posted at September 6, 2008 3:36 PM UTC

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Re: Waldorf on Transport Functors and Connections on Gerbes

Does Konrad plan to work with someone in particular at Berkeley? Teichner, I guess?

Posted by: John Baez on September 7, 2008 3:53 AM | Permalink | Reply to this

Re: Waldorf on Transport Functors and Connections on Gerbes

Does Konrad plan to work with someone in particular at Berkeley? Teichner, I guess?

I suppose Konrad will see this and reply himself. But since it is no secret I guess I can say: yes, Peter Teichner asked him to come to Berkeley.

I suppose there is no lack of other interesting people to interact with, too. Chris Schommer-Pries for instance, whose work I recently mentioned here.

Also, I have been told that some kind of new project has been started involving Mike Hopkins, Jacob Lurie, Stephan Stolz and Peter Teichner who together join forces to think about QFTs. Just imagine. There is some kind of workshop in this context in December or so in New York or so. I forget the details. Konrad will know.

I have been asked by Stephan Stolz to come to Notre Dame for a year end of 2009. Not sure what will happen. My position in Hamburg ends spring 2010. There are a couple of things Konrad and I still want to finish writing up. Will have to be by email for the time being.

Posted by: Urs Schreiber on September 7, 2008 2:01 PM | Permalink | Reply to this

Re: Waldorf on Transport Functors and Connections on Gerbes

Urs wrote:

There is some kind of workshop in this context in December or so in New York or so.

By the way, there’ll be a workshop this week with those guys and a few other, run by Dennis Sullivan. But this workshop is supposed to be on (,1)(\infty,1)-categories, or something like that. Unfortunately I couldn’t make it, because of those Glasgow talks.

Posted by: John Baez on September 8, 2008 6:48 AM | Permalink | Reply to this

Re: Waldorf on Transport Functors and Connections on Gerbes

By the way, there’ll be a workshop this week with those guys and a few other, run by Dennis Sullivan. But this workshop is supposed to be on (,1)(\infty,1)-categories

Ah, possibly that’s the one I meant. I forget the details. Do they have a website?

Posted by: Urs Schreiber on September 9, 2008 11:39 AM | Permalink | Reply to this

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