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Course, academic year 2019/2020
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Algebraic Topology 1 - NMAG409
Title in English: Algebraická topologie 1
Guaranteed by: Mathematical Institute of Charles University (32-MUUK)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019 to 2019
Semester: winter
E-Credits: 5
Hours per week, examination: winter s.:2/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Guarantor: Mgr. Tomáš Salač, Ph.D.
Class: M Mgr. MA
M Mgr. MA > Povinně volitelné
M Mgr. MSTR
M Mgr. MSTR > Povinné
Classification: Mathematics > Topology and Category
Incompatibility : NMAT007
Interchangeability : 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. (05.09.2019)

Credit is awarded for exercises and homework assignments. Completing credit is a condition for doing the exam. The exam has written and oral parts.

Literature - Czech
Last update: Mgr. Dalibor Šmíd, Ph.D. (05.09.2019)
  • E.H. Spanier "Algebraic Topology"
  • M.Aguilar, S.Gitler and C.Prieto "Algebraic Topology from a Homotopical

Viewpoint"

Requirements to the exam -
Last update: Mgr. Dalibor Šmíd, Ph.D. (05.09.2019)

Credit is awarded for exercises and homework assignments. Completing credit is a condition for doing the exam. The exam has written and oral parts.

Syllabus -
Last update: Edoardo Lanari (02.10.2019)

1) Introduction to functorial language;

2) Basic notions of homotopy of maps, homotopy category of spaces;

3) Fundamental group as a functor;

4) Suspensions/loop spaces, wedge sums;

5) Coverings:basic properties, fibrations, monodromy action and

calculations;

6) Seifert-Van Kampen's Theorem with applications.

7) Homology: basic properties, calculations and applications.

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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