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…