For master’s students; Semester 1, Thu. Period 3 · Graduate School of Science and Technology, Niigata University
Textbooks
- J. W. Milnor and J. D. Stashef “Characteristic Classes” Annals of Mathematics Studies
Course contents
- Differentiable manifolds
- Vector bundles, part 1 (definitions, examples)
- Vector bundles, part 2 (the canonical line bundle, sections)
- Vector bundles, part 3 (Euclidean vector bundles, induced bundles)
- Vector bundles, part 4 (Whitney sums, orthogonal complement bundles)
- Singular homology and cohomology (basic definitions, cup products)
- Stiefel-Whitney classes, part 1
- Stiefel-Whitney classes, part 2
- Stiefel-Whitney classes, part 3
- Stiefel-Whitney classes, part 4; Grassmann manifolds, part 1
- Grassmann manifolds, part 2
- Grassmann manifolds, part 3; universal bundles
- Classifying maps; characteristic classes
- H*(Gr;Z/2Z); Pontryagin, Euler, and Chern classes