Algebraic Topology 2 - NMAT008

• Title: Algebraická topologie 2
• Guaranteed by: Mathematical Institute of Charles University (32-MUUK)
• Faculty: Faculty of Mathematics and Physics
• Actual: from 2018
• Semester: summer
• E-Credits: 6
• 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: cancelled
• Language: Czech
• Teaching methods: full-time
• Teaching methods: full-time
• Guarantor: doc. RNDr. Petr Somberg, Ph.D.
• Classification: Mathematics > Topology and Category
• Interchangeability : NMAG532
• Is incompatible with: NMAG532
• Is interchangeable with: NMAG532

Annotation

English

Last update: T_MUUK (23.05.2003)

Special parts. Products in cohomology, duality, sheaves and cohomology of sheaves.

Czech

Last update: ()

Speciální části: Součiny v kohomologii, dualita, svazky a svazkové kohomologie.

Literature

Last update: RNDr. Pavel Zakouřil, Ph.D. (05.08.2002)

1. W.Massey : Singular Homology theory, Springer GTM 70, 1980

2. E.Spanier : Algebraic Topology, McGraw Hill 1966

Syllabus

English

Last update: T_MUUK (23.05.2003)

The functors Tor and Ext. The univesal coefficient theorem for cohomology. Eilenberg-Zilber theorem, Kunneth formula. Products in homology and cohomology. Topological manifolds,Orientation, homology and cohomology of manifolds. Dualities. Poincare duality. DeRham cohomology. Applications of the theory.

Czech

Last update: T_MUUK (23.05.2003)

1. Funktor Tor a Ext.

2. Věta o universálních koeficientech pro kohomologie.

3. Eilenberg - Zilberova věta, Kunnethova formule.

4. Součiny v homologiích a kohomologiích.

5. Topologické variety, orientace.

6. Homologické a kohomologické grupy variet.

7. Duality, Poincareho dualita.

8. DeRhamova kohomologie diferencovatelné variety.

9. Různé aplikace algebraické topologie.