26 citations · 108 across the 19 of their papers we have counts for
24 papers
Blowups of Dirac structures
Ioan Marcut, Andreas Schüßler, Marco Zambon
Given a real, twisted Dirac structure on a smooth manifold , and a closed embedded submanifold of codimension , we characterise when lifts to a smooth…
Normal forms for principal Poisson Hamiltonian spaces
Pedro Frejlich, Ioan Marcut
We prove a normal form theorem for principal Hamiltonian actions on Poisson manifolds around the zero locus of the moment map. The local model is the generalization to Poisson geom…
The Poisson linearization problem for . Part II: The Nash-Moser method
Ioan Marcut, Florian Zeiser
This is the second of two papers, in which we prove a version of Conn's linearization theorem for the Lie algebra . Namely, we…
The Poisson linearization problem for . Part I: Poisson cohomology
Ioan Marcut, Florian Zeiser
This is the first of two papers, in which we prove a version of Conn's linearization theorem for the Lie algebra . Namely, we…
Poisson structures with compact support
Gil R. Cavalcanti, Ioan Marcut
We explicitly construct several Poisson structures with compact support. For example, we show that any Poisson structure on with polynomial coefficients of degree at most tw…
Poisson geometry around Poisson submanifolds
Rui Loja Fernandes, Ioan Marcut
We construct a first order local model for Poisson manifolds around a large class of Poisson submanifolds and we give conditions under which this model is a local normal form. The…
Multiplicative Ehresmann connections
Rui Loja Fernandes, Ioan Marcut
We develop the theory of multiplicative Ehresmann connections for Lie groupoid submersions covering the identity, as well as their infinitesimal counterparts. We construct obstruct…
Poisson structures whose Poisson diffeomorphism group is not locally path-connected
Ioan Marcut
We build examples of Poisson structure whose Poisson diffeomorphism group is not locally path-connected.
The Poisson cohomology of
Ioan Marcut, Florian Zeiser
We compute the smooth Poisson cohomology of the linear Poisson structure associated with the Lie algebra .
Non-degeneracy of the Hofer norm for Poisson structures
Dušan Joksimović, Ioan Marcut
We remark that, as in the symplectic case, the Hofer norm on the Hamiltonian group of a Poisson manifold is non-degenerate. The proof is a straightforward application of tools from…
The homology class of a Poisson transversal
Pedro Frejlich, Ioan Marcut
This note is devoted to the study of the homology class of a compact Poisson transversal in a Poisson manifold. For specific classes of Poisson structures, such as unimodular Poiss…
On local integration of Lie brackets
Alejandro Cabrera, Ioan Marcut, Maria Amelia Salazar
We give a direct, explicit and self-contained construction of a local Lie groupoid integrating a given Lie algebroid which only depends on the choice of a spray vector field liftin…
On dual pairs in Dirac Geometry
Pedro Frejlich, Ioan Marcut
In this note we discuss dual pairs in Dirac geometry. We show that this notion appears naturally when studying the problem of pushing forward a Dirac structure along a surjective s…
Normal forms for Poisson maps and symplectic groupoids around Poisson transversals
Pedro Frejlich, Ioan Marcut
Poisson transversals are those submanifolds in a Poisson manifold which intersect all symplectic leaves transversally and symplectically. In a previous note we proved a normal form…
Reeb-Thurston stability for symplectic foliations
Marius Crainic, Ioan Marcut
We prove a version the local Reeb-Thurston stability theorem for symplectic foliations.
Deformations of log-symplectic structures
Ioan Marcut, Boris Osorno Torres
We describe the space of Poisson bivectors near a log-symplectic structure up to small diffeomorphisms.
The Normal Form Theorem around Poisson Transversals
Pedro Frejlich, Ioan Marcut
We prove a normal form theorem for Poisson structures around Poisson transversals (also called cosymplectic submanifolds), which simultaneously generalizes Weinstein's symplectic n…
On cohomological obstructions to the existence of log symplectic structures
Ioan Marcut, Boris Osorno Torres
We prove that a compact log symplectic manifold has a class in the second cohomology group whose powers, except maybe for the top, are nontrivial. This result gives cohomological o…
Normal forms in Poisson geometry
Ioan Marcut
This thesis studies normal forms for Poisson structures around symplectic leaves using several techniques: geometric, formal and analytic ones. One of the main results (Theorem 2)…
Deformations of the Lie-Poisson sphere of a compact semisimple Lie algebra
Ioan Marcut
A compact semisimple Lie algebra induces a Poisson structure on the unit sphere in . We compute the moduli space of Poisson structures on …
Rigidity around Poisson Submanifolds
Ioan Marcut
We prove a rigidity theorem in Poisson geometry around compact Poisson submanifolds, using the Nash-Moser fast convergence method. In the case of one-point submanifolds (fixed poin…
Formal equivalence of Poisson structures around Poisson submanifolds
Ioan Marcut
Let (M, π ) be a Poisson manifold. A Poisson submanifold gives rise to an algebroid , to which we associate certain chomology groups which control forma…
On the existence of symplectic realizations
Marius Crainic, Ioan Marcut
We give a direct global proof for the existence of symplectic realizations of arbitrary Poisson manifolds.
A Normal Form Theorem around Symplectic Leaves
Marius Crainic, Ioan Marcut
We prove the Poisson geometric version of the Local Reeb Stability (from foliation theory) and of the Slice Theorem (from equivariant geometry). The result is also a generalization…