Sur la symplectisation de structures bihamiltoniennes

✍ Scribed by Fani Petalidou

• Publisher: Elsevier Science
• Year: 2000
• Tongue: French
• Weight: 198 KB
• Volume: 124
• Category: Article
• ISSN: 0007-4497
• DOI: 10.1016/s0007-4497(00)00132-9

✦ Synopsis

We study the problem of the symplectization of a bihamiltonian manifold (M, Λ 0 , Λ 1 ) and we establish, in the case where M is of odd dimension, the sufficient conditions of this construction in the neighbourhood of a generic point of M. In addition, we give several types of bihamiltonian structures, among which that of Poisson-Nijenhuis, which are locally symplectizable. Finally, we give the sufficient and necessary conditions so that a 2-cobord of the Λ 0 -cohomology should be a Poisson tensor.