Characteristic classes of vector bundles are invariants which have been applied universally in geometry. Basic properties of cohomology required for the introduction of the characteristic classes, vector bundles and their related notions will be explained.
- to get deeper understanding of cohomology of topological spaces.
- to understand vector bundles and related notions.
Verified computation, interval arithmetic, Newton's method, fixed point theorems
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
vector bundle
Course schedule | Required learning | |
---|---|---|
Class 1 | review of homology | Details will be provided during each class session |
Class 2 | review of cohomology | Details will be provided during each class session |
Class 3 | definition of vector bundles | Details will be provided during each class session |
Class 4 | Remannian metric | Details will be provided during each class session |
Class 5 | maps of vector bundles and subbundles | Details will be provided during each class session |
Class 6 | orientation on vector bundle | Details will be provided during each class session |
Class 7 | theorem of Leray-Hirsch | Details will be provided during each class session |
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
non required
John Milnor, James D. Stasheff, Characteristic Classes. Volume 76 (Annals of Mathematics Studies), Princeton University Press.
Ichiro Tamura, Differential Topology, Iwanami.
Assignments (100%).
Knowledge on topology (MTH.B341) and manifolds (MTH.B301, MTH.B302) are required.