Grothendieck Groups of Poisson Vector Bundles
| dc.creator | Ginzburg, Viktor L. | |
| dc.date | 2000-09-13 | |
| dc.date.accessioned | 2026-07-07T04:37:22Z | |
| dc.date.available | 2026-07-07T04:37:22Z | |
| dc.description | A new invariant of Poisson manifolds, a Poisson K-ring, is introduced. Hypothetically, this invariant is more tractable than such invariants as Poisson (co)homology. A version of this invariant is also defined for arbitrary algebroids. Basic properties of the Poisson K-ring are proved and the Poisson K-rings are calculated for a number of examples. In particular, for the zero Poisson structure the K-ring is the ordinary K-theory of the manifold and for the dual space to a Lie algebra the K-ring is the ring of virtual representations of the Lie algebra. It is also shown that the K-ring is an invariant of Morita equivalence. Moreover, the K-ring is a functor on a category, the weak Morita category, which generalizes the notion of Morita equivalence of Poisson manifolds. | |
| dc.description | 32 pages | |
| dc.identifier | https://arxiv.org/abs/math/0009124 | |
| dc.identifier | http://arxiv.org/abs/math/0009124 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59924 | |
| dc.subject | Differential Geometry | |
| dc.subject | K-Theory and Homology | |
| dc.subject | Symplectic Geometry | |
| dc.title | Grothendieck Groups of Poisson Vector Bundles | |
| dc.type | text |