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Course, academic year 2023/2024
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Algebraic Topology 2 - NMAG532
Title: Algebraická topologie 2
Guaranteed by: Mathematical Institute of Charles University (32-MUUK)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023
Semester: summer
E-Credits: 5
Hours per week, examination: summer s.:2/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: English, Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: Roman Golovko, Ph.D.
Class: M Mgr. MSTR
M Mgr. MSTR > Povinně volitelné
Classification: Mathematics > Topology and Category
Incompatibility : NMAT008
Interchangeability : NMAT008
Is interchangeable with: NMAT008
Annotation -
Basic theory of higher homotopy groups. Coefficients for singular (co)homology and the corresponding algebraic theory of derived functors. Deeper homotopy properties of manifolds.
Last update: T_MUUK (27.04.2016)
Course completion requirements

There will be several homeworks. As a requirement to take the final exam students must submit

solutions to at least one homework. The final exam will be an oral exam.

Last update: Golovko Roman, Ph.D. (26.02.2021)
Literature -

A. Hatcher: Algebraic Topology.Cambridge University Press, 2002.

E. H. Spanier: Algebraic Topology. Springer, 1989.

Last update: Golovko Roman, Ph.D. (26.02.2021)
Requirements to the exam

For the oral part of the exam it is necessary to know the whole content of lecture.

You will get time to write a preparation for the oral part which the knowledge of definitions, theorems and their proofs is tested.

We test as well the understanding to the lecture, you will have to prove an easy theorem which follows from statements from the lecture.

Last update: Golovko Roman, Ph.D. (26.02.2021)
Syllabus -

Quillen model categories, homotopy category, derived functors, simplicial sets, chain complexes, homotopy algebra, homotopy limits and colimits.

Last update: Šmíd Dalibor, Mgr., Ph.D. (29.01.2022)
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