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Differential topology

Code: 92947
ECTS: 5.0
Lecturers in charge: izv. prof. dr. sc. Zvonko Iljazović - Lectures
English level:

1,0,0

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.
Load:

1. komponenta

Lecture typeTotal
Lectures 45
* Load is given in academic hour (1 academic hour = 45 minutes)
Description:
COURSE AIMS AND OBJECTIVES: Introduce students to topological and differentiable aspects of manifolds, vector bundles, and vector fields on manifolds and relate this matter with geometry, mathematical analysis and differential equations.

COURSE DESCRIPTION AND SYLLABUS (by weeks):
1. Topological manifolds
2. Differentiable and smooth manifolds.
3. Examples of topological and smooth manifolds.
4. Vector bundles.
5. Tangent and normal bundle of a manifold.
6. Vector fields.
7. Sard's theorem.
8. Whitney's theorem, Stoke's theorem.
9. Introduction to Morse theory.
10. Cohomology and characteristic classes (only introductory).
11. Selected topics on vector fields on spheres.
12. Euler-Poincare's theorem.
13. Gauss-Bonnet's theorem.
Literature:
  1. J. Milnor: Topology from the Differentiable Viewpoint
  2. S. Lang: Introduction to Differentiable Manifolds
  3. J. M. Lee: Introduction to Smoothe Manifolds
  4. M. Hirsch: Differential Topology
  5. T. Bröcker, K. Jänich: Einführung in die Differential Topologie
Prerequisit for:
Enrollment :
Passed : Metric spaces
3. semester
Izborni predmeti 5, 6, 7 - Regular study - Mathematical Statistics

4. semester
Izborni predmeti 5, 6, 7 - Regular study - Mathematical Statistics
Consultations schedule: