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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 2014 to 2016
Semester:	winter
E-Credits:	5
Hours per week, examination:	winter 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:	Czech, English
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	Mgr. Martin Doubek, Ph.D. doc. RNDr. Petr Somberg, 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
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.

Literature - Czech

Last update: Mgr. Dalibor Šmíd, Ph.D. (05.09.2019)

1. A. Hatcher : Algebraic Topology, Cambridge University Press, 2002, k dispozici on-line

2. R. Bott, L. Tu : Differential Forms In Algebraic Topology, Springer-Verlag New York Inc, 1995

Syllabus -

Last update: Mgr. Dalibor Šmíd, Ph.D. (05.09.2019)

1. Introduction to homotopy theory, retraction, homotopy type of a space.

2. Fundamental group of a topological space, covering spaces, universal cover.

3. Simplicial, singular and CW homology.

4. Long exact sequence, Excision, Mayer-Vietoris sequence.

5. Additional topics based on time and interests.