Split Canonical Relations

A Lagrangian subspace L of a weak symplectic vector space is called split if it has an isotropic (hence Lagrangian) complement. When the structure strong, sufficient for to have closed complement, which can then be moved become isotropic. The purpose this note develop theory compositions and reductions canonical relations spaces. We give conditions on coisotropic C V imply that induced relation from C/C ? split, and, these, we find compose well. prove arising in Poisson sigma model field theoretical approach are giving description groupoids integrating manifolds terms relations.