1. komponenta

Lecture type	Total
Lectures	45

* Load is given in academic hour (1 academic hour = 45 minutes)

COURSE AIMS AND OBJECTIVES:
Introduce the students to the basic ideas and methods of algebraic topology, and illustrate some simple results obtained using this methods.

COURSE DESCRIPTION AND SYLLABUS:
Subjects by weeks:
1. Homotopy and the homotopy type.
2. Paths. Fundamental group.
3. Fundamental group of the circle. Some applications.
4. Van Kampen's theorem.
5. Covering spaces. Lifting paths, homotopies and mappings.
6. Classification of covering spaces.
7. -complexes, simplicijal complexes, CW-complexes.
8. Simplicijal and singular homology.
9. Homotopy invariance of homology.
10. Homology exact sequence and the Excision theorem.
11. Homology axioms.
12. Applications 1. Jordan's simple closed curve theorem. Invariance of domain.
13. Applications 2. Lefschetz fixed point theorem.

Enrollment :
Passed : General topology

Mandatory course - Regular study - Theoretical Mathematics