We study a class of deformations of infinite-dimensional Poisson manifoldsof hydrodynamic type which are of interest in the theory of Frobenius manifolds. Weprove 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 con-jecture of B. Dubrovin about the triviality of homogeneous formal deformations of theabove manifolds.
|Number of pages||24|
|Journal||Communications in Mathematical Physics|
|Publication status||Published - 2005|
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics