First Order Differential Calculus on Manifolds
Alexandre De Paris
A program of the course at the 4-th Italian Diffiety School,
(Forino, July 17-29, 2000)
(Preliminary version)
- 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.
The exam has been passed by the following students:
- 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.