Last updated June 21, 2001
Calculus in commutative algebras
  1. Algebro-geometric duality in the theory of smooth manifolds.
  2. Linear differential operators in commutative algebras, basic functors of differential calculus.
  3. Representing object: differential forms and jets in the category of modules.
  4. The de Rham and Spencer complexes.
  5. The Poincare \delta-lemma.
  6. The Nijenhuis bracket, the complexes related to flat connections.
  7. The Schouten bracket and Poisson algebras, the complexes related to Poisson structures.
  8. An algebraic model of the Hamiltonian formalism.
Questions and suggestions should go to J. S. Krasil'shchik, josephk @ diffiety.ac.ru.