| Algebraic and differential topology (2) |
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| Teaching Staff in Charge |
| Prof. ANDRICA Dorin, Ph.D., dandrica@math.ubbcluj.ro |
| Aims |
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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. |
| Content |
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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. |
| References |
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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 |
| Assessment |
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Exam. |