19032 Lecture

SoSe 13: (V) ErgänzungsM Ausgew. Forschungsthemen:Characteristic Classes"

Pavle Blagojevic

Information for students

Zielgruppe:

Students who have completed a first course in algebraic topology.

Comments

Inhalt:

  1. 1. Fiber bundles (definition, morphism and first examples)
  2. 2. Vector bundles (definition, a lot of examples, cross section, parallelizable manifolds)
  3. 3. Euclidean vector bundles (definition, existence of a Euclidean metric)
  4. 4. Operations on Vector bundles (restriction, pull-back, Cartesian product, Whitney sum, Orthogonal complement, Normal bundle etc.)
  5. 5. Stiefel--Whitney classes (introduction via axioms and first calculations)
  6. 6. Applications: Immersion
  7. 7. Stiefel--Whitney numbers
  8. 8. Steenrod Algebra (introduction via axioms and first calculations)
  9. 9. Grassmann manifold and universal bundles
  10. 10. Cell structure of the Grassmanian
  11. 11. Cohomology of the Grassmanina
  12. 12. Construction of Stiefel--Whitney classes
  13. 13. Application: Solving open problem by using Stiefel--Whitney classes
  14. 14. Construction of Steenrod Algebra
  15. 15. Oriented bundles and Euler class
  16. 16. The Thom isomorphism theorem
  17. 17. Applications: Computations over smooth manifolds
  18. 18. Complex vector bundles
  19. 19. Chern classes
  20. 20. Pontrjagin classes
  21. 21. Chern numbers and Pontrjagin numbers
  22. 22. The Oriented cobordism ring and Thom space
close

Suggested reading

Literatur:

Milnor, John W. and Stasheff, James D.: "Characteristic classes", Princeton Univ. Press.

12 Class schedule

Regular appointments

Wed, 2013-04-10 14:00 - 16:00

Lecturers:
Dr. Pavle Blagojevic

Location:
SR 1/A2 Seminarraum (Arnimallee 2 / 4)

Wed, 2013-04-17 14:00 - 16:00

Lecturers:
Dr. Pavle Blagojevic

Location:
SR 1/A2 Seminarraum (Arnimallee 2 / 4)

Wed, 2013-04-24 14:00 - 16:00

Lecturers:
Dr. Pavle Blagojevic

Location:
SR 1/A2 Seminarraum (Arnimallee 2 / 4)

Wed, 2013-05-08 14:00 - 16:00

Lecturers:
Dr. Pavle Blagojevic

Location:
SR 1/A2 Seminarraum (Arnimallee 2 / 4)

Wed, 2013-05-15 14:00 - 16:00

Lecturers:
Dr. Pavle Blagojevic

Location:
SR 1/A2 Seminarraum (Arnimallee 2 / 4)

Wed, 2013-05-22 14:00 - 16:00

Lecturers:
Dr. Pavle Blagojevic

Location:
SR 1/A2 Seminarraum (Arnimallee 2 / 4)

Wed, 2013-05-29 14:00 - 16:00

Lecturers:
Dr. Pavle Blagojevic

Location:
SR 1/A2 Seminarraum (Arnimallee 2 / 4)

Wed, 2013-06-05 14:00 - 16:00

Lecturers:
Dr. Pavle Blagojevic

Location:
SR 1/A2 Seminarraum (Arnimallee 2 / 4)

Wed, 2013-06-12 14:00 - 16:00

Lecturers:
Dr. Pavle Blagojevic

Location:
SR 1/A2 Seminarraum (Arnimallee 2 / 4)

Wed, 2013-06-19 14:00 - 16:00

Lecturers:
Dr. Pavle Blagojevic

Location:
SR 1/A2 Seminarraum (Arnimallee 2 / 4)

Wed, 2013-06-26 14:00 - 16:00

Lecturers:
Dr. Pavle Blagojevic

Location:
SR 1/A2 Seminarraum (Arnimallee 2 / 4)

Wed, 2013-07-03 14:00 - 16:00

Lecturers:
Dr. Pavle Blagojevic

Location:
SR 1/A2 Seminarraum (Arnimallee 2 / 4)

Subjects A - Z