|Algebraic and differential topology (2)|
|Teaching Staff in Charge|
|Prof. ANDRICA Dorin, Ph.D., firstname.lastname@example.org|
The main purpose of the course consists in the presentation of the basic concepts, notions and results concerning de Rham coomology of differential forms on a differentiable manifold. From many points of view the topic of this course is a natural continuation of the material presented for this master class in the first semester. At the seminar the students will complete by individual papers some topics presented in the course.
1. Elements of de Rham cohomology. Determinants, volumes and Hodge' operator. Differential forms. Integration of differential forms and Stokes' theorem. De Rham
cohomology spaces and first computations. The Mayer-Vietoris sequence and applications.
Poincare' duality. the connection with the singular homoilogy: de Rham theorem.
2. Other theories of cohomology. Shaves and preshaves. The shaves cohomology. Some
classical cohomology theories: Alexander-Spanier, singular cohomology, Cech' cohomology.
The de Rham model. Multiplicity structures in cohomology.
1. Andrica,D.,Critical Point Theory and Some Applications, University of Ankara, 1994
2. Bredon,G.E.,Topology and Geometry, Springer-Verlag, 1993
3. Conlon,L.,Diferentiable manifolds. A First Course, Birkhauser,1993
4. Godbillon,C.,Elements de topologie algebrique, Hermann, Paris, 1971