Chern-Weil Constructions on $Ψ$DO Bundles
| dc.creator | Paycha, Sylvie | |
| dc.creator | Rosenberg, Steven | |
| dc.date | 2003-01-17 | |
| dc.date | 2003-02-21 | |
| dc.date.accessioned | 2026-07-07T04:54:30Z | |
| dc.date.available | 2026-07-07T04:54:30Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/math/0301185 | |
| dc.identifier | http://arxiv.org/abs/math/0301185 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66276 | |
| dc.subject | Differential Geometry | |
| dc.subject | Mathematical Physics | |
| dc.subject | Analysis of PDEs | |
| dc.title | Chern-Weil Constructions on $Ψ$DO Bundles | |
| dc.type | text |