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Course, academic year 2022/2023
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Algebraic Topology 1 - NMAG409
Title: Algebraická topologie 1
Guaranteed by: Mathematical Institute of Charles University (32-MUUK)
Faculty: Faculty of Mathematics and Physics
Actual: from 2021 to 2022
Semester: winter
E-Credits: 5
Hours per week, examination: winter s.:2/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
Virtual mobility / capacity: no
State of the course: taught
Language: English, Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: Mgr. Tomáš Salač, Ph.D.
Class: M Mgr. MA
M Mgr. MA > Povinně volitelné
M Mgr. MSTR > Povinné
Classification: Mathematics > Topology and Category
Incompatibility : NMAT007
Interchangeability : NMAT007
Is interchangeable with: NMAT007
Annotation -
Last update: T_MUUK (13.05.2013)
Foundations of homotopy and singular homology theories. CW-complexes and their homology. Basic cohomology theory. Applications.
Course completion requirements -
Last update: Mgr. Dalibor Šmíd, Ph.D. (21.10.2021)

Every two weeks a homework assignment will be given with the two weeks deadline. Students can send their solutions by e-mail or bring them in a hand written form after a lecture. The condition for the credit is the submission of 40% of correct solutions. Each problem will have a percentage mark. The overall percentage will be calculated as a weighted sum of percentages for each homework. The final assignment percentage mark will also be considered in the final course mark as an evaluation of student activity during the semester.

Literature -
Last update: Roman Golovko, Ph.D. (22.09.2020)

A. Hatcher "Algebraic Topology"

E.H. Spanier "Algebraic Topology"

Requirements to the exam -
Last update: Roman Golovko, Ph.D. (18.09.2020)

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 -
Last update: Roman Golovko, Ph.D. (18.09.2020)
  • Homotopy and homotopy type,
  • Cell complexes,
  • Fundamental group,
  • Van Kampen's theorem,
  • Covering spaces,
  • Classification of covering spaces, deck transformation group,
  • Singular homology, simplicial homology,
  • Exact sequences and excision,
  • Equivalence of simplicial and singular homology,
  • Mayer-Vietoris sequence,
  • Cellular homology,
  • Axioms for homology.

Entry requirements -
Last update: Mgr. Dalibor Šmíd, Ph.D. (17.09.2019)

Basics of general topology covered by the course Topology and category theory (NMAG332), basic algebraic structures (groups, rings, modules). Homological algebra welcome but not required.

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