Chern-Weil Constructions on $Ψ$DO Bundles

Details Chern-Weil Constructions on $Ψ$DO Bundles Chern-Weil Constructions on $Ψ$DO Bundles

2003-01-17

arxiv.org/abs/math/0301185v2

Mathematics

Differential Geometry

Scientific paper

We construct Chern-Weil classes on infinite dimensional vector bundles with structure group contained in the algebra $\cl[\leq 0](M, E)$ of non-positive order classical pseudo-differential operators acting on a finite rank vector bundle $E$ over a closed manifold $M$. Mimicking the finite dimensional Chern-Weil construction, we replace the ordinary trace on matrices by linear functionals on $\cl[\leq 0] (M, E)$ built from the leading symbols of the operators. The corresponding Chern classes vanish for loop groups, but a weighted trace construction yields a non-zero class perviously constructed by Freed. For loop spaces, the structure group reduces to a gauge group of bundle automorphisms, and we produce non-vanishing universal Chern classes in all degrees, using a universal connection theorem for these bundles.

Affiliated with

Also associated with

No associations

Rating

Chern-Weil Constructions on $Ψ$DO Bundles 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 Chern-Weil Constructions on $Ψ$DO Bundles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Chern-Weil Constructions on $Ψ$DO Bundles will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-585891