"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science

Homotopy theory
Code
Semes-
ter
Hours: C+S+L
Credits
Type
Section
MG011
8
2+2+0
8
optional
Matematică-Informatică
Teaching Staff in Charge
Prof. ANDRICA Dorin, Ph.D., dandrica@math.ubbcluj.ro
Aims
The course construct the main mathematical instruments necessary in the homotopic study of topological spaces.
Content
1. The fundamental group, fiber bundles and covering spaces.
2. High order homotopy groups.
3. The exact homotopy sequence of a topological pair.
4. The homotopy groups of a product of two spaces.
5. Some representations of homotopy groups as direct sums.
6. The homotopy groups of a fiber bundle and a covering spaces.
7. The homotopy groups of some particular spaces.
References
1. Andrica,D.,Pintea,C.,Elemente de teoria omotopiei cu aplicatii la studiul punctelor critice, Editura Mirton, Timisoara, 2002
2. Greenberg, M.J., Harper, J.R., Algebraic Topology. A first course, Addison-Wesley, 1981.
3. Godbillon, C., Elements de topologie algebrique, Hermann, Paris, 1971.
4. Husemoller, D., Fibre Bundles, McGrow-Hill Book Company.
5. Sze Tzen Hu, Homotopy Theory, Academic Press New York and London, 1959.
Assessment
Exam.