- Garant předmětu:
- Department of Physics
A study of modern mathematical and theoretical physics requires one to acquire an ever increasing knowledge of mathematical apparautus. The main goal of this course is to acquaint students with basic methods used in algebraic topology, namely elements of category theory, homototopies, homological algebra and cohomology. An important objective is to enhance the mathematical language by concepts appearing universally across disciplines like differential geometry and abstract algebra. During excercise sessions, students will try practical calculations of introduced mathematical structures.
- Syllabus of lectures:
1. Homotopy relation
2. Fundamental group
3. Categories and functors
4. Cellular and simplicial complexes
5. Simplicial and singular homology and their relation
6. de Rham cohomology, Poincaré lemma and duality
7. Sheaves and associated Čech cohomology
8. Čech - de Rham cohomology
9. Cohomology of Lie algebras
- Syllabus of tutorials:
Practical calculations of introduced mathematical structures, proofs of simpler propositions.
- Study Objective:
- Study materials:
 Hatcher, Allen: Algebraic Topology. Cambridge University Press, 2002.
 Bott, Raoul, and Tu, Loring W.: Differential forms in algebraic topology. Vol. 82. Springer Science & Business Media, 2013.
 Tu, Loring W.: Differential geometry: connections, curvature, and characteristic classes. Vol. 275. Springer, 2017.
 Spanier, Edwin H.: Algebraic topology. Vol. 55. No. 1. Springer Science & Business Media, 1989.
 Knapp, Elias, and Knapp Anthony W.: Lie groups, Lie algebras, and cohomology. Vol. 34. Princeton University Press, 1988.
- Further information:
- No time-table has been prepared for this course
- The course is a part of the following study plans: