Open Access
December, 2001 Grothendieck Groups of Poisson Vector Bundles
V.L. Ginzburg
J. Symplectic Geom. 1(1): 121-170 (December, 2001).


A new invariant of Poisson manifolds, a Poisson K-ring, is introduced. Evidence is given that this invariant is more tractable than such invariants as Poisson (co)homology. A version of this invariant is also defined for arbitrary Lie algebroids. Basic properties of the Poisson K-ring areproved 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 K0-ring 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.


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V.L. Ginzburg . "Grothendieck Groups of Poisson Vector Bundles." J. Symplectic Geom. 1 (1) 121 - 170, December, 2001.


Published: December, 2001
First available in Project Euclid: 12 August 2004

zbMATH: 1032.53072
MathSciNet: MR1959580

Rights: Copyright © 2001 International Press of Boston

Vol.1 • No. 1 • December, 2001
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