0000000000639998

AUTHOR

Franco Magri

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On deformation of Poisson manifolds of hydrodynamic type

2001

We study a class of deformations of infinite-dimensional Poisson manifolds of hydrodynamic type which are of interest in the theory of Frobenius manifolds. We prove two results. First, we show that the second cohomology group of these manifolds, in the Poisson-Lichnerowicz cohomology, is ``essentially'' trivial. Then, we prove a conjecture of B. Dubrovin about the triviality of homogeneous formal deformations of the above manifolds.

Class (set theory)Pure mathematicsConjectureDeformation (mechanics)Nonlinear Sciences - Exactly Solvable and Integrable SystemsGroup (mathematics)FOS: Physical sciencesStatistical and Nonlinear PhysicsType (model theory)Poisson distributionMAT/07 - FISICA MATEMATICATrivialityMathematics::Geometric TopologyCohomologysymbols.namesakeDeformation of Poisson manifoldsPoisson-Lichnerowicz cohomologysymbolsPoisson manifolds Poisson-Lichnerowicz cohomology Infinite-dimensional manifolds Frobenius manifoldsMathematics::Differential GeometryExactly Solvable and Integrable Systems (nlin.SI)Mathematics::Symplectic GeometryMathematical PhysicsMathematics
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