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Algebraic topology

Code: 92918
ECTS: 5.0
Lecturers in charge: prof. dr. sc. Zvonko Iljazović
English level:


All teaching activities will be held in Croatian. However, foreign students in mixed groups will have the opportunity to attend additional office hours with the lecturer and teaching assistants in English to help master the course materials. Additionally, the lecturer will refer foreign students to the corresponding literature in English, as well as give them the possibility of taking the associated exams in English.

1. komponenta

Lecture typeTotal
Lectures 45
* Load is given in academic hour (1 academic hour = 45 minutes)
Introduce the students to the basic ideas and methods of algebraic topology, and illustrate some simple results obtained using this methods.

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.
  1. A. Hatcher: Algebraic Topology
  2. C. R. F. Massey: Algebraic Topology
  3. C. O. Christenson, W. L. Voxman: Aspects of Topology
  4. J. R. Munkres: Elements of Algebraic Topology
  5. J. G. Hocking, G.S. Young: Topology
  6. E. H. Spanier: Algebraic Topology
Prerequisit for:
Enrollment :
Passed : General topology
3. semester
Mandatory course - Regular study - Theoretical Mathematics
Consultations schedule: