| Course: | MTH 3481 (Topology III) |
| Instructor: | Alex Suciu |
| Time and Place: | Mon. & Wed. at 5:15 -- 6:45 PM, in 544 NI |
| Office Hours: | Mon. & Wed. at 11:45 AM -- 12:45 PM, in 441 LA, or by appointment |
| Prerequisites: | MTH 3107 (Topology II) |
| Textbook: | Topology and Geometry, by Glen Bredon, Springer-Verlag, GTM #139 |
| Grade: | Based on problem sets and a final exam |
| Cohomology Theory | Cohomology of chain complexes, simplicial and singular cohomology, universal coefficients theorems, cross products and the Künneth formula, cup and cap products. |
| Duality in Manifolds | The orientation bundle, Poincaré duality, Lefschetz duality, Alexander duality, Euler class, Lefschetz numbers, Gysin sequence, intersection form, signature, plumbing. |
| Homotopy Theory | Higher homotopy groups, cofibrations, fibrations, homotopy sequences, homotopy groups of Lie groups and associated manifolds, Hurewicz theorem, Whitehead theorem, Eilenberg-MacLane spaces, obstruction theory. |
| Bundles and Characteristic Classes | Classifying spaces, cohomology of classifying spaces, Stiefel-Whitney classes, Pontrjagin classes, Chern classes, spectral sequences. |
| Homework 1 | Chapter V, section 8, pp. 284-285 | # 2, 3, 4, 7 |
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| Homework 2 |
Chapter VI, section 3, p. 321
Chapter VI, section 4, p. 334 Chapter VI, section 5, p. 338 |
# 1
# 3 # 1, 2, 3 |
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| Department of Mathematics | Office: | 441 Lake Hall |
| Northeastern University | Phone: | (617) 373-4456 |
| Boston, MA, 02115 | Email: |
 alexsuciu@neu.edu
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Created: March 1, 2000 Last modified: April 19, 2000
URL: http://www.math.neu.edu/~suciu/mth3481/top3.sp00.html |