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August 21, 2009

Notes on Differential Nonabelian Cohomology

Posted by Urs Schreiber

I have begun to prepare on my personal nnLab page notes on stuff that I am working on. Some of it is in a state that should be readable and on which I would enjoy getting comments. This I want to present here.

The entry point for the technical material is here:

- nnLab/schreiber/differential nonabelian cohomology

Behind the above link you find pointers to more information.

So far the material available there concerns the abstract definition of differential cohomology in an arbitrary (,1)(\infty,1)-topos and the derivation from that of the notion of \infty-Cartan-Ehresmann connection on principal \infty-bundles.

Posted at August 21, 2009 7:06 PM UTC

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k-dimensional interval objects??

aka cubes?

Posted by: jim stasheff on August 22, 2009 2:14 AM | Permalink | Reply to this

Re: k-dimensional interval objects??

Okay, I changed the wording in the standout box abstract here to this:

We start with a basic simple definition of differential nonabelian cohomology that works in great generality in any (,1)(\infty,1)-topos equipped with a notion of disk-shaped cobordisms. In low categorical dimension this reproduces the description in [BaSc] [ScWaI, ScWaIII]

Somewhere else I should say that whether these “disk shaped cobordism objects” are modeled as globes (as we did in the above references), as simplicies (as I do now), or as cubes (as in [MaPiI, MaPiII MaPiIII]) is a question of technical implementation and not of principle.

Posted by: Urs Schreiber on August 22, 2009 7:51 AM | Permalink | Reply to this

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