## 603 Citations

### BATALIN-VILKOVISKY AND GRAVITY ALGEBRAS ON POISSON MANIFOLDS WITH SEMISIMPLE MODULAR SYMMETRY

- Mathematics
- 2021

We study the “twisted” Poincaré duality of smooth Poisson manifolds, and show that, if the modular symmetry is semisimple, that is, the modular vector is diagonalizable, there is a mixed complex…

### A local Torelli theorem for log symplectic manifolds

- Mathematics
- 2020

We establish a local model for the moduli space of holomorphic symplectic structures with logarithmic poles, near the locus of structures whose polar divisor is normal crossings. In contrast to the…

### On Poisson structures of hydrodynamic type and their deformations

- Mathematics
- 2016

Systems of quasilinear partial differential equations of the first order, known as hydrodynamic type systems, are one of the most important classes of nonlinear partial differential equations in the…

### Normal forms of Poisson structures

- Mathematics
- 2011

These notes arise from a minicourse given by the two authors at the Summer School on Poisson Geometry, ICTP, 2005. The main reference is our recent monograph “Poisson structures and their normal…

### An introduction to some novel applications of Lie algebra cohomology in mathematics and physics

- Mathematics
- 2001

This paper has been partially supported by a research grant from the MEC, Spain
(PB96-0756). J. C. P. B. wishes to thank the Spanish MEC and the CSIC for an FPI grant.

### An introduction to some novel applications of Lie algebra cohomology and physics

- Mathematics
- 1998

After a self-contained introduction to Lie algebra cohomology, we present some recent applications in mathematics and in physics. Contents:
1. Preliminaries: L_X, i_X, d
2. Elementary differential…

### Gravity algebra structure on the negative cyclic homology of Calabi–Yau algebras

- MathematicsJournal of Geometry and Physics
- 2020

### Basic forms and Morse–Novikov cohomology of Lie groupoids

- MathematicsMathematische Nachrichten
- 2018

Given a basic closed 1‐form on a Lie groupoid G , the Morse–Novikov cohomology groups Hθn(G) are defined in this paper. They coincide with the usual de Rham cohomology groups HdRn(G) when θ is exact…

### Morse-Novikov Cohomology for Blow-ups of Complex Manfiolds

- Mathematics
- 2018

We define the weight {\theta}-sheaf R_{X,\theta} and reinterpret Morse-Novikov cohomology via sheaf theory. We establish a theorem of Leray-Hirsch type for Morse-Novikov cohomology. Eventually, using…

### Complete and vertical lifts of Poisson vector fields and infinitesimal deformations of Poisson tensor

- Mathematics
- 2018

In this paper we prove that both complete and vertical lifts of a Poisson vector field from a Poisson manifold $(M, \pi)$ to its tangent bundle $(TM, \pi_{TM})$ are also Poisson. We use this fact to…