Stability of leaves of Dirac structures

par Karandeep Singh (KU Leuven)

vendredi 11 sept. 2026, 14:00 → 15:00 Europe/Paris

Salle Fokko du Cloux (Bat. Braconnier)

Dirac structures were introduced by T. Courant, and can be used to describe classical phase spaces in the presence of constraints. 

A Dirac structure over a manifold M is a subbundle of TM + T*M satisfying an integrability condition, and it foliates M by presymplectic manifolds of possibly different dimensions. Examples include Poisson structures, symplectic structures and regular foliations.

Given a compact leaf of the characteristic foliation, it is natural to consider the stability of the (presymplectic) leaf under small deformations of the Dirac structure. In the case that the Dirac manifold is Poisson, M. Crainic and R. Fernandes gave a sufficient condition in terms of Lie algebroid cohomology. In this talk, we generalize their results to the Dirac setting.