24 citations · 26 across the 8 of their papers we have counts for
9 papers
Deformation of singular foliations, 1: Local deformation cohomology
Philippe Monnier, Nguyen Tien Zung
In this paper we introduce the notion of deformation cohomology for singular foliations and related objects (namely integrable differential forms and Nambu structures), and study i…
Rigidity of actions on presymplectic manifolds
Philippe Monnier
We prove the rigidity of presymplectic actions of a compact semisimple Lie algebra on a presymplectic manifold of constant rank in the local and global case. The proof uses an abst…
Rigidity of Hamiltonian actions on Poisson manifolds
Eva Miranda, Philippe Monnier, Nguyen Tien Zung
This paper is about the rigidity of compact group actions in the Poisson context. The main resut is that Hamiltonian actions of compact semisimple type are rigid. We prove it via a…
Normal forms of vector fields on Poisson manifolds
Philippe Monnier, Nguyen Tien Zung
We study formal and analytic normal forms of radial and Hamiltonian vector fields on Poisson manifolds near a singular point.
Linearization of Poisson brackets
Rui Loja Fernandes, Philippe Monnier
We review the linearization of Poisson brackets and related problems, in the formal, analytic and smooth categories.
A cohomology attached to a function
Philippe Monnier
In this paper, we study a certain cohomology attached to a smooth function, which arose naturally in Poisson geometry. We explain how this cohomology depends on the function, and w…