Seminario Geometría, Mecánica y Control
Reduction of contact manifolds
Ponente: Bartosz M. Zawora ()Fecha: jueves 19 de marzo de 2026 - 12:00Online: Zoom. ID: 810 9248 3225; Código acceso: 183643
Resumen:
The Marsden-Meyer-Weinstein (MMW) reduction theorem for contact manifolds has brought significant attention of many researchers. The first generalisation of the classical MMW reduction theorem for a contact manifold was proven by C. Albert in 1989. However, this result applies only to coorientable contact manifolds and depends on the contact form choice within its conformal class. Since then, numerous results on the reduction theorem have appeared, including a recent reduction scheme for the case when the contact manifold is non-coorientable, devised by K. Grabowska and J. Grabowski, which introduces new conditions and geometric tools to address the limitations of Albert’s work.
In my talk, I will present the contact analogue of the classical symplectic MMW reduction. I will begin with a survey of the fundamental notions and results of symplectic and contact geometry, with particular emphasis on reduction techniques in the presence of Lie group symmetries. Then, after a concise overview of the symplectic MMW reduction, I will formulate the corresponding MMW reduction procedure for contact manifolds. In addition, I will define and discuss a modified coadjoint orbit in the projective space of a dual Lie algebra and I will discuss the contact analogue of the classical symplectic orbit reduction introduced by Marle in 1976.
