| Course: | MTH 3481 (Topology III) |
| Instructor: | Alex Suciu |
| Time and Place: | Tue. & Th. at 11:45 AM - 1:15 PM, in 509 LA |
| Office Hours: | 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 | Problems 2, 3, 4, 7 |
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| Homework 2 | Chapter VI, section 3, p. 321
Chapter VI, section 4, p. 334 |
Problems 1, 2, 3
Problems 3, 4 |
| Homework 3 | Chapter VI, section 4, p. 334
Chapter VI, section 5, p. 338 |
Problems 7, 8
Problems 1, 3, 4, 5 |
| Homework 4 | Chapter VI, section 7, p. 348
Chapter VI, section 8, p. 355 Chapter VI, section 10, p. 366 |
Problems 1, 3
Problems 6, 7 Problems 4, 5, 7 |
| Homework 5 | Chapter VI, section 15, p. 412
Chapter VII, section 5, p. 450 Chapter VII, section 10, p. 480 Chapter VII, section 12, p. 497 |
Problems 1, 5
Problems 1, 2 Problems 1, 3 Problem 1 |
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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
5, 1998 Last modified: June
11, 1998
URL: http://www.math.neu.edu/~suciu/mth3481/top3.sp98.html |