Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Forgot your password?
• Apply for membership

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeOct 26th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexa little remark at _[[nonabelian Stokes theorem]]_, still to be expanded

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

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeOct 26th 2012
   • (edited Oct 26th 2012)
   • PermaLink
   Author: zskoda
   Format: MarkdownItexMaybe 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).

   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).

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeOct 26th 2012
   • (edited Oct 26th 2012)
   • PermaLink
   Author: Urs
   Format: MarkdownItexOkay, I have added a pointer to * _Smooth Functors vs. Differential Forms_ ([arXiv:0802.0663](http://arxiv.org/abs/0802.0663))

   Okay, I have added a pointer to

   • Smooth Functors vs. Differential Forms (arXiv:0802.0663)
4. • CommentRowNumber4.
   • CommentAuthorEric
   • CommentTimeOct 28th 2012
   • PermaLink
   Author: Eric
   Format: MarkdownItexI 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.

   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.

5. • CommentRowNumber5.
   • CommentAuthorEric
   • CommentTimeOct 28th 2012
   • (edited Oct 28th 2012)
   • PermaLink
   Author: Eric
   Format: MarkdownItexIs 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...

   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…

6. • CommentRowNumber6.
   • CommentAuthorDavidRoberts
   • CommentTimeOct 28th 2012
   • (edited Oct 28th 2012)
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexNever mind.

   Never mind.

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeOct 29th 2012
   • (edited Oct 29th 2012)
   • PermaLink
   Author: Urs
   Format: MarkdownItex> 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 infinity-groupoid|smooth n-groupoid]] of a [[smooth infinity-group|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.

   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.

8. • CommentRowNumber8.
   • CommentAuthorUrs
   • CommentTimeNov 2nd 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded more references <a href="https://ncatlab.org/nlab/revision/diff/nonabelian+Stokes+theorem/5">diff</a>, <a href="https://ncatlab.org/nlab/revision/nonabelian+Stokes+theorem/5">v5</a>, <a href="https://ncatlab.org/nlab/show/nonabelian+Stokes+theorem">current</a>

   added more references

   diff, v5, current