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Course, academic year 2023/2024
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Algebraic Topology 1 - NMAT007
Title: Algebraická topologie 1
Guaranteed by: Mathematical Institute of Charles University (32-MUUK)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: winter
E-Credits: 6
Hours per week, examination: winter s.:2/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: cancelled
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: doc. RNDr. Petr Somberg, Ph.D.
Classification: Mathematics > Topology and Category
Interchangeability : NMAG409
Is incompatible with: NMAG409
Is interchangeable with: NMAG409
Annotation -
Last update: SMID/MFF.CUNI.CZ (01.10.2008)
Foundations of homotopy and singular homology theories. CW-complexes and their homology. Basic cohomology theory. Applications.
Literature - Czech
Last update: SMID/MFF.CUNI.CZ (01.10.2008)

1. A. Hatcher : Algebraic Topology, Cambridge University Press, 2002, k dispozici on-line

2. R. Bott, L. Tu : Differential Forms In Algebraic Topology, Springer-Verlag New York Inc, 1995

Syllabus -
Last update: doc. RNDr. Petr Somberg, Ph.D. (10.09.2013)

1. Introduction to homotopy theory, retraction, homotopy type of a space.

2. Fundamental group of a topological space, covering spaces, universal cover.

4. Simplicial and singular homology.

5. Long exact sequence, Excision, Mayer-Vietoris sequence.

6. Additional topics based on time and interests.

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