Course Information Course Information
| Course: | MTH 3414: Bundles and Characteristic Classes |
| Instructor: | Alex Suciu |
| Time and Place: | Mon. 7:15 - 8:45 PM, in 509LA, Th. 10:30 - 12:00 in 544NI |
| Office Hours: | By appointment |
| Prerequisites: |
MTH 3105--Topology I, MTH 3107--Topology II,
MTH 3400--Geometry I, MTH 3481--Topology III. |
| Textbooks: |
Fibre Bundles, by Dale Husemoller
Characteristic Classes, by John Milnor and James Stasheff |
| Grade: | Based on problem sets and class participation |
Course DescriptionThe course is meant as an introduction to fiber bundles and characteristic classes. It supposes a certain familiarity with the basic objects of topology and geometry, e.g., manifolds, cell complexes, homology and homotopy.
We will first discuss principal bundles (Milnor's construction of universal bundles, the homotopy classification of G-bundles) and vector bundles (new vector bundles out of old ones, local coordinate description). We will work out many examples, e.g., bundles over spheres, Lie groups and homogeneous manifolds, gauge groups.
We will then study the cohomology of classifying spaces, i.e., characteristic classes: Grassmann manifolds and Stiefel-Whitney classes; oriented bundles, obstructions, Gysin and Wang sequences, the Thom isomorphism, and the Euler class; complex bundles, Chern classes, and Pontrjagin classes. Applications will include obstructions to embeddings of manifolds, vector fields on spheres, cobordism theory, Hirzebruch index formula, exotic spheres.
Homework Assignments| Handout 1 | Homework 1 | Homework 2 | Homework 3 |
| Department of Mathematics | Office: | 441 Lake Hall | Messages: | (617) 373-2450 |
| Northeastern University | Phone: | (617) 373-4456 | Fax: | (617) 373-5658 |
| Boston, MA, 02115 | Email: |
 a.suciu@neu.edu
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Directions |
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Created: September 28, 2000 Last modified: December 2, 2000
URL: https://web.northeastern.edu/suciu/mth3414/bundles.f00.html |