Alexandre De Paris

A program of the course at the 4-th Italian Diffiety School,

(Forino, July 17-29, 2000)

(

- Tangent vectors and absolute and relative vector fields. D functor
- The flow of a vector field. Lie derivative of vector fields. Commutators and Lie algebrae
- Tangent covectors and differential forms. Tensors. Main operations on tensors. Algebra of differential forms
- Behaviour of differential forms and covariant tensors with respect to differentiable mappings of manifolds. Lie derivatives of covariant tensors.
- Exterior differential and de Rham cohomology
- Cartan's formula and homotopy property of de Rham cohomology
- Integration theory as de Rham cohomology

Passing the exam during the school required 9 solved problems. To pass the exam by email one should solve 11 problems.

- Diego Catalano
- Giovanna Ilardi
- Emanuele Castagna
- Stefania Donadio
- Rossella Piscopo
- Massimiliano Malgieri
- Beniamino Cappelletti

Questions and suggestions should go to Jet NESTRUEV, jet @ diffiety.ac.ru.