Bigraded differential operators in poisson geometry

Abstract

In this thesis we develop bigraded calculus for differential operators with applications to some problems in Poisson geometry, related to singular foliations. The goal of this work is to give a unified approach to the Schouten - Frölicher-Nijenhuis-Ehresmann calculus on fibred and foliated manifolds and apply this approach to the study of infinitesimal automorphisms and first cohomology of Poisson manifolds with singular symplectic foliations. Some results on computing Poisson cohomology in the regular case can be found, for example, in [38, 39, 31, 32, 8]. In some special singular cases, Poisson cohomology has been studied in [5, 22, 23, 24, 25].