98 citations · 413 across the 37 of their papers we have counts for
31 papers · 1 filter
Poisson Manifolds of Compact Types with an Appendix by Joshua Mundinger
Marius Crainic, Rui Loja Fernandes, David Martínez Torres +1
We develop the theory of Poisson and Dirac manifolds of compact types, a broad generalization in Poisson and Dirac geometry of compact Lie algebras and Lie groups. We establish key…
Haefliger's differentiable cohomology
Luca Accornero, Marius Crainic
We review Haefliger's differentiable cohomology for the pseudogroup of diffeomorphisms of . We investigate the structure needed to define such a cohomology, which, re…
The transverse density bundle and modular classes of Lie groupoids
Marius Crainic, João Nuno Mestre
In this note we revisit the notions of transverse density bundle and of modular classes of Lie algebroids and Lie groupoids; in particular, we point out that one should use the tra…
From PDEs to Pfaffian fibrations
Francesco Cattafi, Marius Crainic, Maria Amelia Salazar
We explain how to encode the essential data of a PDE on jet bundle into a more intrinsic object called Pfaffian fibration. We provide motivations to study this new notion and show…
Lie Pseudogroups à la Cartan
Marius Crainic, Ori Yudilevich
We present a modern formulation of Élie Cartan's structure theory for Lie pseudogroups and prove a reduction theorem that clarifies the role of Cartan's systatic system. The paper…
Orbispaces as differentiable stratified spaces
Marius Crainic, João Nuno Mestre
We present some features of the smooth structure, and of the canonical stratification on the orbit space of a proper Lie groupoid. One of the main features is that of Morita invari…