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

English

Last update: T_MUUK (27.04.2016)

Basic theory of higher homotopy groups. Coefficients for singular (co)homology and the corresponding algebraic theory of derived functors. Deeper homotopy properties of manifolds.

Czech

Last update: T_MUUK (27.04.2016)

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

Course completion requirements

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

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.

Literature

English

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

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

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

Czech

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

“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

Requirements to the exam

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

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.

Syllabus

English

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

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