8 jan 2019 -- 11:00
Sala Riunioni DipMat, Salerno
Abstract.
In this talk, we discuss the notions of duality in Jacobi geometry. In the first part, based on joint work with A. Blaga, M. A. Salazar, and C. Vizman, we introduce the notion of a contact dual pair as a pair of Jacobi morphisms defined on the same contact manifold and satisfying a certain orthogonality condition. The central motivating example is formed by the source and the target maps of a contact groupoid. One of the main results is the characteristic leaf correspondence theorem for contact dual pairs which finds immediate application to the context of reduction theory. Indeed any free and proper contact groupoid action naturally gives rise to a contact dual pair and so the characteristic leaf correspondence yields a new insight into the global contact reduction as described by Zambon and Zhu. In the second part, based on joint work with J. Schnitzer, we discuss (weak) dual pairs in Dirac-Jacobi geometry. Our main result is an explicit construction of self-dual pairs for Dirac-Jacobi structures. As applications of this result we give a global and more conceptual construction of contact realizations and present a different approach to the normal form theorem around Dirac-Jacobi transversals.