Differentiable Cohomology of Gauge Groups

Details Differentiable Cohomology of Gauge Groups Differentiable Cohomology of Gauge Groups

2000-11-11

arxiv.org/abs/math/0011069v1

Mathematics

Differential Geometry

24 pages

Scientific paper

We give a definition of differentiable cohomology of a Lie group G (possibly infinite-dimensional) with coefficients in any abelian Lie group. This differentiable cohomology maps both to the cohomology of the group made discrete and to Lie algebra cohomology. We show that the secondary characteristic classes of Beilinson lead to differentiable cohomology classes with coefficients in C*. These may be viewed as an enrichment of the Chern-Simons differential forms. By transgression, classes in differentiable cohomology of a Lie group G lead to differentiable cohomology classes for gauge groups Map(M,G). These classes generalize the central extensions of loop groups. We also discuss holomorphic cohomology of complex Lie groups as the natural place to construct secondary classes. We present several conjectures relating the above cohomology classes to the differential forms of Bott-Shulman-Stasheff.

Affiliated with

Also associated with

No associations

Rating

Differentiable Cohomology of Gauge Groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Differentiable Cohomology of Gauge Groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Differentiable Cohomology of Gauge Groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-452650