The n-Category Café

Skip to the Main Content

Note:These pages make extensive use of the latest XHTML and CSS Standards. They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. Moreover, many posts use MathML, which is, currently only supported in Mozilla. My best suggestion (and you will thank me when surfing an ever-increasing number of sites on the web which have been crafted to use the new standards) is to upgrade to the latest version of your browser. If that's not possible, consider moving to the Standards-compliant and open-source Mozilla browser.

« nLab Migration | Main | Higher-Dimensional Algebra VII: Groupoidification »

August 21, 2009

Notes on Differential Nonabelian Cohomology

Posted by Urs Schreiber

I have begun to prepare on my personal $n$Lab 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:

- $n$Lab/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 $(\infty,1)$-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

TrackBack URL for this Entry:   https://golem.ph.utexas.edu/cgi-bin/MT-3.0/dxy-tb.fcgi/2040

Some Related Entries

Search for other entries:

• Asymptotics of the Magnitude of Metric Spaces — Aug 13, 2009
• Question about ∞-Colimits — Aug 10, 2009
• Question on Synthetic Differential Forms — Aug 03, 2009
• Groupoidfest 09 — Aug 02, 2009
• Question on Models for (∞,1)-Functor Categories — Jul 29, 2009
• Verity on Descent for Strict ω-Groupoid Valued Presheaves — Jul 23, 2009
• Laubinger on Lie Algebras for Frölicher Groups — Jul 01, 2009
• Cohomology and Homotopy — Jun 26, 2009

2 Comments & 0 Trackbacks

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 $(\infty,1)$-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

Post a New Comment