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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeOct 26th 2012

a little remark at nonabelian Stokes theorem, still to be expanded

• CommentRowNumber2.
• CommentAuthorzskoda
• CommentTimeOct 26th 2012
• (edited Oct 26th 2012)

Maybe some basic references would be helpful for orientation. I knew of some references about some generalizations of Stokes to some nonabelian setups, but I am not sure how many of them where indeed about what is described in this entry, i.e. the case of Lie algebras and parallel transport (at least one or two were about that case, this I remember).

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeOct 26th 2012
• (edited Oct 26th 2012)

Okay, I have added a pointer to

• CommentRowNumber4.
• CommentAuthorEric
• CommentTimeOct 28th 2012

I made a minor formatting change to the sidebar. I noticed when I was revising geometry pf physics that the Contexts would display all listed contexts together when you hover over it. I thought it would be better to display only the specific item you hovered over. Now, the “Differential geometry” and “$\infty$-Lie theory” can display independently. This is a change I also made to geometry of physics that was lost when my changes were rolled back.

• CommentRowNumber5.
• CommentAuthorEric
• CommentTimeOct 28th 2012
• (edited Oct 28th 2012)

Is there a higher version of Stokes theorem involving higher parallel transport? I mean something that might relate $(n+1)$-transport to $n$-transport on a boundary for $0\le n\le D-1$. Something like that…

• CommentRowNumber6.
• CommentAuthorDavidRoberts
• CommentTimeOct 28th 2012
• (edited Oct 28th 2012)

Never mind.

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeOct 29th 2012
• (edited Oct 29th 2012)

I made a minor formatting change to the sidebar. I noticed when I was revising geometry pf physics that the Contexts would display all listed contexts together when you hover over it. I thought it would be better to display only the specific item you hovered over.

Ah, thanks, that’s indeed better. I should remember to use this code next time.

Is there a higher version of Stokes theorem involving higher parallel transport?

Yes, there are higher analogs in arbitrary degree. As I briefly indicate in the entry, the nonabelian Stokes theorem may be regarded as part of the $n$-functoriality of an $n$-functor from a path n-groupoid to the delooping smooth n-groupoid of a smooth n-group.

It gets increasingly tedious to write it out explicitly, though. Partial formulas for $n = 3$ are in the literature. For instance in our appendix we do part of it when we discuss 3-form curvature.