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Course, academic year 2019/2020
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Algebraic Topology 2 - NMAG532
Title in English: Algebraická topologie 2
Guaranteed by: Mathematical Institute of Charles University (32-MUUK)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019 to 2019
Semester: summer
E-Credits: 5
Hours per week, examination: summer 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. MSTR
M Mgr. MSTR > Povinně volitelné
Classification: Mathematics > Topology and Category
Incompatibility : NMAT008
Interchangeability : NMAT008
Annotation -
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.
Literature -
Last update: Mgr. Martin Doubek, Ph.D. (10.09.2013)

A. Hacher : Algebraic Topology, available on the web

J. P. May : A Concise Course in Algebraic Topology, available on the web

C. A. Weibel : An Introduction to Homological Algebra, Cambridge (1994)

A. Cartan, S. Eilenberg : Homological algebra, Princeton (1956)

R. M. Switzer : Algebraic Topology, Springer (1975)

R. Bott, L. W. Tu : Differential Forms in Algebraic Topology, Springer (1982)

Syllabus -
Last update: doc. RNDr. Petr Somberg, Ph.D. (23.05.2019)

1. Homotopy groups, Hurewicz and Whitehead theorem.

2. Singular homology with coefficients, universal coefficient theorem, Tor.

3. Derived functors.

4. Künneth formula.

5. Singular cohomology, universal coefficient theorem, Ext.

6. Homology of manifolds, Poincaré duality.

7. De Rham cohomology.

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