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. Fiber bundles (definition, morphism and first examples)
- 2. Vector bundles (definition, a lot of examples, cross section,
parallelizable manifolds)
- 3. Euclidean vector bundles (definition, existence of a Euclidean metric)
- 4. Operations on Vector bundles (restriction, pull-back, Cartesian product,
Whitney sum, Orthogonal complement, Normal bundle etc.)
- 5. Stiefel--Whitney classes (introduction via axioms and first calculations)
- 6. Applications: Immersion
- 7. Stiefel--Whitney numbers
- 8. Steenrod Algebra (introduction via axioms and first calculations)
- 9. Grassmann manifold and universal bundles
- 10. Cell structure of the Grassmanian
- 11. Cohomology of the Grassmanina
- 12. Construction of Stiefel--Whitney classes
- 13. Application: Solving open problem by using Stiefel--Whitney classes
- 14. Construction of Steenrod Algebra
- 15. Oriented bundles and Euler class
- 16. The Thom isomorphism theorem
- 17. Applications: Computations over smooth manifolds
- 18. Complex vector bundles
- 19. Chern classes
- 20. Pontrjagin classes
- 21. Chern numbers and Pontrjagin numbers
- 22. The Oriented cobordism ring and Thom space
close
- 1. Fiber bundles (definition, morphism and first examples)
- 2. Vector bundles (definition, a lot of examples, cross section, parallelizable manifolds)
- 3. Euclidean vector bundles (definition, existence of a Euclidean metric)
- 4. Operations on Vector bundles (restriction, pull-back, Cartesian product, Whitney sum, Orthogonal complement, Normal bundle etc.)
- 5. Stiefel--Whitney classes (introduction via axioms and first calculations)
- 6. Applications: Immersion
- 7. Stiefel--Whitney numbers
- 8. Steenrod Algebra (introduction via axioms and first calculations)
- 9. Grassmann manifold and universal bundles
- 10. Cell structure of the Grassmanian
- 11. Cohomology of the Grassmanina
- 12. Construction of Stiefel--Whitney classes
- 13. Application: Solving open problem by using Stiefel--Whitney classes
- 14. Construction of Steenrod Algebra
- 15. Oriented bundles and Euler class
- 16. The Thom isomorphism theorem
- 17. Applications: Computations over smooth manifolds
- 18. Complex vector bundles
- 19. Chern classes
- 20. Pontrjagin classes
- 21. Chern numbers and Pontrjagin numbers
- 22. The Oriented cobordism ring and Thom space
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
Wed, 2013-04-17 14:00 - 16:00
Wed, 2013-04-24 14:00 - 16:00
Wed, 2013-05-08 14:00 - 16:00
Wed, 2013-05-15 14:00 - 16:00
Wed, 2013-05-22 14:00 - 16:00
Wed, 2013-05-29 14:00 - 16:00
Wed, 2013-06-05 14:00 - 16:00
Wed, 2013-06-12 14:00 - 16:00
Wed, 2013-06-19 14:00 - 16:00
Wed, 2013-06-26 14:00 - 16:00
Wed, 2013-07-03 14:00 - 16:00
Inhalt:
1. Fiber bundles (definition, morphism and first examples) 2. Vector bundles (definition, a lot of examples, cross section, parallelizable manifolds) 3. Euclidean vector bundles ...
read more