Classification of \(b^m\)-Nambu structures of top degree (Q1704653)

This paper gives a classification of \(b^m\) Nambu structures via \(b^m\)-cohomology. Let us recall that a \(b\)-manifold is an even-dimensional Poisson manifold with transversality condition. When the transversality condition is relaxed in a way such that the critical hypersurface is still a smooth manifold, we obtain a \(b^m\) Poisson manifold. In this work, the authors generalize the \(b\)-setting to the Nambu world and classify the corresponding structures. In particular, they prove an extension of Moser's classification theorem. Moreover, a geometrical interpretation to the Mazzeo-Melrose decomposition theorem is obtained.