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
• Guarantor: Roman Golovko, Ph.D.
• Teacher(s): 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

English

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)

Czech

Základy teorie vyšších homotopických grup. Koeficienty pro singulární (ko)homologii a příslušná algebraická teorie derivovaných funktorů. Cup součin. Hlubší homotopické vlastnosti variet.

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

English

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

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

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

Czech

“Notes on simplicial homotopy theory” A.Joyal and M.Tierney, notes available at http://www.mat.uab.cat/~kock/crm/hocat/advanced-course/Quadern47.pdf

“Model Categories”, M.Hovey

“Simplicial homotopy theory”, P.Goerss and R.Jardine

Last update: Šmíd Dalibor, Mgr., Ph.D. (23.01.2020)

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

English

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)