Classification of bm-Nambu structures of top degree

Abstract

In this paper, we classify bm-Nambu structures via bm-cohomology. The complex of bm-forms is an extension of the De Rham complex, which allows us to consider singular forms. bm-Cohomology is well understood thanks to Scott (2016) [12], and it can be expressed in terms of the De Rham cohomology of the manifold and of the critical hypersurface using a Mazzeo–Melrose-type formula. Each of the terms in bm-Mazzeo–Melrose formula acquires a geometrical interpretation in this classification. We also give equivariant versions of this classification scheme.