Pedro Frejlich
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View article: Dirac products and concurring Dirac structures
Dirac products and concurring Dirac structures Open
We discuss in this note two dual canonical operations on Dirac structures $L$ and $R$ -- the \emph{tangent product} $L \star R$ and the \emph{cotangent product} $L \circledast R$. Our first result gives an explicit description of the leave…
View article: Coregular submanifolds and Poisson submersions
Coregular submanifolds and Poisson submersions Open
In this paper, we analyze submersions with Poisson fibres . These are submersions whose total space carries a Poisson structure, on which the ambient Poisson structure pulls back, as a Dirac structure, to Poisson structures on each individ…
View article: Normal forms for principal Poisson Hamiltonian spaces
Normal forms for principal Poisson Hamiltonian spaces Open
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 geometry of the classical minimal coupling construction from sy…
View article: Coregular submanifolds and Poisson submersions
Coregular submanifolds and Poisson submersions Open
We analyze \emph{submersions with Poisson fibres}. These are submersions whose total space carries a Poisson structure, on which the ambient Poisson structure pulls back, as a Dirac structure, to Poisson structures on each individual fibre…
View article: Morita Invariance of Intrinsic Characteristic Classes of Lie Algebroids
Morita Invariance of Intrinsic Characteristic Classes of Lie Algebroids Open
In this note, we prove that intrinsic characteristic classes of Lie\nalgebroids - which in degree one recover the modular class - behave\nfunctorially with respect to arbitrary transverse maps, and in particular are\nweak Morita invariants…
View article: The Homology Class of a Poisson Transversal
The Homology Class of a Poisson Transversal Open
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 Poisson structures and Poisson manifolds with closed leaves, we …
View article: A note on the symplectic topology of $b$-manifolds
A note on the symplectic topology of $b$-manifolds Open
A Poisson manifold $(M^{2n},\p)$ is $b$-symplectic if $\bigwedge^n\p$ is transverse to the zero section. In this paper we apply techniques native to Symplectic Topology to address questions pertaining to $b$-symplectic manifolds. We provid…
View article: On realizations of Dirac structures by closed two-forms
On realizations of Dirac structures by closed two-forms Open
In this short note we prove that any Dirac structure can be realized as the push-forward of a presymplectic form via a surjective submersion, and moreover, that this submersion fits into a full dual pair of Dirac structures, a notion we in…