Noncommutative Geometry of Phase Space
  We investigate the geometric, algebraic and homologic structures related with Poisson structure on a smooth manifold. Introduce a noncommutative foundations of these structures for a Poisson algebra. Introduce and investigate noncommutative Bott connection on a foliated manifold using the algebraic definition of submanifold and quotient manifold. Develop an algebraic construction for the reduction of a degenerated Poisson algebra. 
Zakaria Giunashvili