Subjects

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Algebraic Topology 1 - NMAT007

Title:	Algebraická topologie 1
Guaranteed by:	Mathematical Institute of Charles University (32-MUUK)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2018
Semester:	winter
E-Credits:	6
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:	cancelled
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	doc. RNDr. Petr Somberg, Ph.D.
Classification:	Mathematics > Topology and Category
Interchangeability :	NMAG409
Is incompatible with:	NMAG409
Is interchangeable with:	NMAG409

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Annotation -

Foundations of homotopy and singular homology theories. CW-complexes and their homology. Basic cohomology theory. Applications.

Last update: SMID/MFF.CUNI.CZ (01.10.2008)

Literature - Czech

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

Last update: SMID/MFF.CUNI.CZ (01.10.2008)

Syllabus -

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

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

4. Simplicial and singular homology.

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

6. Additional topics based on time and interests.

Last update: Somberg Petr, doc. RNDr., Ph.D. (10.09.2013)