Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · math/0004065

Duality and modular class of a Nambu-Poisson structure

R. Ibanez·M. de Leon·B. Lopez·J. C. Marrero·E. Padron
View original source ↗Read source document ↗Export metadata ↓

Abstract

In this paper we introduce cohomology and homology theories for Nambu-Poisson manifolds. Also we study the relation between the existence of a duality for these theories and the vanishing of a particular Nambu-Poisson cohomology class, the modular class. The case of a regular Nambu-Poisson structure and some singular examples are discussed.

Explore related subjects

math.SGmath-phmath.MP

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

R. Ibanez, M. de Leon, B. Lopez, J. C. Marrero, E. Padron. 2000-04-11. Duality and modular class of a Nambu-Poisson structure. https://doi.org/10.1088/0305-4470%2F34%2F17%2F306

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Algebra of the Infrared with Elliptic Curve-Valued Potential

We study an extension of the algebra of the infrared to curve--valued potentials, focusing on the elliptic curve case. Given a finite configuration of points on an elliptic curve, we construct associated \(L_\infty\)-algebra. Adding an extra point produces a directed \(A_\infty\)-algebra and an \(L_\infty\)-morphism to their directed Hochschild deformation complexes. Maurer--Cartan elements of the \(L_\infty\)-algebra determine \(A_\infty\)-deformations of the directed algebra. We formulate a conjectural comparison between Maurer--Cartan deformations of the directed algebra and the directed Fukaya--Seidel category associated to compatible finite collections of thimbles.

math.SG↗
arXiv2026

Moment Lagrangians, unobstructedness and symplectic groupoids

Moment Lagrangian $L_μ$ is a Lagrangian in $T^*G^- \times Y^- \times Y$ associated to a Hamiltonian $G$-space $Y$ with a moment map $μ$. In this paper, we prove that $L_μ$ is tautologically unobstructed under mild assumptions on $Y$. As a key ingredient in the proof, we constructed a new symplectic groupoid structure on $T^*G^- \times Y^- \times Y$ over $G\times Y$ for which $L_μ$ is simultaneously the unit and the fixed locus of the inversion, which might be of independent interest.

math.SG↗
arXiv2026

Functors from Lagrangian correspondences for wrapped sheaf categories

We consider the category of sheaves on a manifold with microsupport in a singular conic Lagrangian, and more generally microsheaves on the Lagrangian skeleton of a Weinstein manifold with stop, which are equivalent to ind-completions of partially wrapped Fukaya categories. Compact objects in these categories are obtained as wrappings of constructible sheaves with perfect stalks; they correspond to objects built from exact Lagrangians in finitely many steps. We give a microlocal criterion on constructible (micro)sheaves with perfect (micro)stalks which guarantees that the corresponding wrapped sheaves induce integral kernels that preserve compact objects of these categories. This generalizes a result of Gao on Lagrangian correspondences between fully wrapped Fukaya categories.

math.SG↗