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. © Springer-Verlag 2004.
Degiovanni, L., Magri, F., Sciacca, V. (2005). On deformation of Poisson manifolds of hydrodynamic type. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 253(1), 1-24 [10.1007/s00220-004-1190-8].
On deformation of Poisson manifolds of hydrodynamic type
MAGRI, FRANCO;
2005
Abstract
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. © Springer-Verlag 2004.
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