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Algebraic Topology 2 - NMAG532

Title:	Algebraická topologie 2
Guaranteed by:	Mathematical Institute of Charles University (32-MUUK)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2014 to 2016
Semester:	summer
E-Credits:	5
Hours per week, examination:	summer 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. MSTR M Mgr. MSTR > Povinně volitelné
Classification:	Mathematics > Topology and Category
Incompatibility :	NMAT008
Interchangeability :	NMAT008
Is interchangeable with:	NMAT008

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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. Dalibor Šmíd, Ph.D. (23.01.2020)

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.