* higher gauge theory
@ 2005-11-29 7:11 John Baez
2005-12-01 21:13 ` John Baez
0 siblings, 1 reply; 2+ messages in thread
From: John Baez @ 2005-11-29 7:11 UTC (permalink / raw)
To: categories
Dear Categorists -
Here's a new paper:
http://math.ucr.edu/home/baez/higher.pdf
http://math.ucr.edu/home/baez/higher.ps
John Baez and Urs Schreiber
Higher Gauge Theory
Just as gauge theory describes the parallel transport of point
particles using connections on bundles, higher gauge theory
describes the parallel transport of 1-dimensional objects (e.g.
strings) using 2-connections on 2-bundles. A 2-bundle is a
categorified version of a bundle: that is, one where the fiber
is not a manifold but a category with a suitable smooth structure.
Where gauge theory uses Lie groups and Lie algebras, higher gauge
theory uses their categorified analogues: Lie 2-groups and Lie
2-algebras. We describe a theory of 2-connections on principal
2-bundles and explain how this is related to Breen and Messing's
theory of connections on nonabelian gerbes. The distinctive
feature of our theory is that a 2-connection allows parallel
transport along paths and surfaces in a parametrization-independent
way. In terms of Breen and Messing's framework, this requires
that the `fake curvature' must vanish. In this paper we summarize
the main results of our theory without proofs.
Fans of Lie groupoids may enjoy the "smooth 2-groupoid" used in this
paper.
Best,
jb
^ permalink raw reply [flat|nested] 2+ messages in thread
* Re: higher gauge theory
2005-11-29 7:11 higher gauge theory John Baez
@ 2005-12-01 21:13 ` John Baez
0 siblings, 0 replies; 2+ messages in thread
From: John Baez @ 2005-12-01 21:13 UTC (permalink / raw)
To: categories
Dear Categorists -
> Here's a new paper:
>
> http://math.ucr.edu/home/baez/higher.pdf
> http://math.ucr.edu/home/baez/higher.ps
>
> John Baez and Urs Schreiber
> Higher Gauge Theory
... but if that's too long, you can see the results in
distilled form here:
http://math.ucr.edu/home/baez/union/
This is my talk at this weekend's Union College conference on
categories, topology and commutative algebra. Hope to see some
of you there!
Best,
jb
^ permalink raw reply [flat|nested] 2+ messages in thread
end of thread, other threads:[~2005-12-01 21:13 UTC | newest]
Thread overview: 2+ messages (download: mbox.gz / follow: Atom feed)
-- links below jump to the message on this page --
2005-11-29 7:11 higher gauge theory John Baez
2005-12-01 21:13 ` John Baez
This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for NNTP newsgroup(s).