On deformation ofPoisson manifolds of Hydrodynamic type

Vincenzo Sciacca; Luca Degiovanni; Franco Magri

On deformation ofPoisson manifolds of Hydrodynamic type

Vincenzo Sciacca, Luca Degiovanni, Franco Magri

Matematica e Informatica

Research output: Contribution to journal › Article › peer-review

37 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	1-24
Number of pages	24
Journal	Communications in Mathematical Physics
Volume	253
Publication status	Published - 2005

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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title = "On deformation ofPoisson manifolds of Hydrodynamic type",

abstract = "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.",

author = "Vincenzo Sciacca and Luca Degiovanni and Franco Magri",

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journal = "Communications in Mathematical Physics",

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T1 - On deformation ofPoisson manifolds of Hydrodynamic type

AU - Sciacca, Vincenzo

AU - Degiovanni, Luca

AU - Magri, Franco

PY - 2005

Y1 - 2005

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10447/28650

M3 - Article

VL - 253

SP - 1

EP - 24

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

ER -