Decomposability of a Poisson Tensor Could Be a Stable Phenomenon

Dufour, Jan-Paul

Afr. Diaspora J. Math. (N.S.), Tome 9 (2009) no. 2, p. 74-81 / Harvested from Project Euclid

Résumé

In this paper, we develop one of the questions raised by the author in the mini-course he gave at the conference Geometry and Physics V held at the University Cheikh Anta Diop, Dakar in May 2007). Let $\Pi$ be a Poisson tensor on a manifold $M.$ We suppose that it is decomposable in a neighborhood $U$ of a point $m,$ i.e. we have $\Pi=X\wedge Y$ on $U$ where $X$ and $Y$ are two vector fields. We will exhibit examples where every Poisson tensor near enough $\Pi$ seems to be also decomposable in a neighborhood of a point which can be chosen arbitrarily near $m$; and this works even if $M$ has a big dimension. This idea is a consequence of a cohomology calculation which can be interesting by itself.

Détail

Publié le : 2009-09-15
Classification:  Poisson tensor,  Lichnerowicz-Poisson cohomology,  decomposability,  division property,  isolated singularity,  53D17,  14Fxx