CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2020/2021

# Algebraic Topology

The course is not on the list Without time-table
Code Completion Credits Range
02ALTO Z,ZK 5
Lecturer:
Tutor:
Supervisor:
Department of Physics
Synopsis:

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.

Requirements:
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:

Key references:

[1] Hatcher, Allen: Algebraic Topology. Cambridge University Press, 2002.

[2] Bott, Raoul, and Tu, Loring W.: Differential forms in algebraic topology. Vol. 82. Springer Science &amp; Business Media, 2013.

Recommended references:

[3] Tu, Loring W.: Differential geometry: connections, curvature, and characteristic classes. Vol. 275. Springer, 2017.

[4] Spanier, Edwin H.: Algebraic topology. Vol. 55. No. 1. Springer Science &amp; Business Media, 1989.

[5] Knapp, Elias, and Knapp Anthony W.: Lie groups, Lie algebras, and cohomology. Vol. 34. Princeton University Press, 1988.

Note:
Further information:
No time-table has been prepared for this course
The course is a part of the following study plans:
Data valid to 2021-01-16
For updated information see http://bilakniha.cvut.cz/en/predmet6216406.html