19032
Vorlesung
SoSe 13: (V) ErgänzungsM Ausgew. Forschungsthemen:Characteristic Classes"
Pavle Blagojevic
Hinweise für Studierende
Zielgruppe:
Students who have completed a first course in algebraic topology.
Kommentar
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
Schließen
- 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
Literaturhinweise
Literatur:
Milnor, John W. and Stasheff, James D.: "Characteristic classes", Princeton Univ. Press.
12 Termine
Regelmäßige Termine der Lehrveranstaltung
Mi, 10.04.2013 14:00 - 16:00
Mi, 17.04.2013 14:00 - 16:00
Mi, 24.04.2013 14:00 - 16:00
Mi, 08.05.2013 14:00 - 16:00
Mi, 15.05.2013 14:00 - 16:00
Mi, 22.05.2013 14:00 - 16:00
Mi, 29.05.2013 14:00 - 16:00
Mi, 05.06.2013 14:00 - 16:00
Mi, 12.06.2013 14:00 - 16:00
Mi, 19.06.2013 14:00 - 16:00
Mi, 26.06.2013 14:00 - 16:00
Mi, 03.07.2013 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 ...
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