Course: | MTH 3483--Topics in Topology |
Instructor: | Alex Suciu |
Time and Place: | Mon. & Wed., 7:15 - 8:45 PM, in 544 NI |
Office Hours: | Mon. & Wed., 4:00 - 5:00 PM, in 441 LA |
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 |
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.
Notes & Homework 1 |
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Homework 2 |
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Homework 3 |
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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: | alexsuciu@neu.edu | Directions |
Created: August 20, 1998 Last modified: December 27, 1998
URL: http://www.math.neu.edu/~suciu/mth3483/toptop.f98.html |