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MAT 531: Topology & Geometry, II
Stony Brook Spring 2006 |
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The final exam has been graded. If you are unable to stop by my office today (05/10), you can take a look at your exam on Wednesday or Friday of next week (05/17,19).
Notes on Vector Bundles,
Course Overview
Detailed solutions to:
final exam,midterm
From last year:
homework assignments, course summary,
midterm, and
final exam, prepared by
Vladlen Timorin.
Name:
Aleksey Zinger
E-mail: azinger@math
Phone: 432-8618
Office: Math Tower 3-117
Office Hours: Wed 9-12
| Date | Topic | Read | Problem Set |
| 1/24 | Smooth Manifolds | 1.1-1.6 | PS #1 |
| 1/26 | Partitions of Unity, Tangent Vectors | 1.7-1.18 | |
| 1/31 | Tangent Bundle, Submanifolds | 1.19-1.25,1.27-1.30 | PS #2 |
| 2/2 | Inverse Function Theorem | 1.30-1.36 | |
| 2/7 | Implicit Function Theorems | 1.37-1.43 | PS #3 |
| 2/9 | Vector Fields | 1.44-1.53 | |
| 2/14 | Frobenius Theorem | 1.54-1.64 | PS #4 |
| 2/16 | Differential Forms | 2.1-2.18 | |
| 2/21 | The Differential | 2.14-2.23 | PS #5 |
| 2/23 | Lie Derivative | 2.24-2.32 | |
| 2/28 | de Rham Cohomology of Rn | 4.13-4.15,4.18,4.19 4.4-4.6 |
PS #6 |
| 3/2 | Integration on Singular Chains | 4.6,4.7,4.16,4.17 4.1-4.3 | |
| 3/7 | Integration on Oriented Manifolds | 4.1-4.3,4.8-4.10 | |
| 3/9 | Review | ||
| 3/14 | Midterm | ||
| 3/16 | (Co-)Chain Complexes | 5.16,5.17 | PS #7 |
| 3/21 | Sheafs and Presheafs | 5.1-5.3,5.5-5.8 | |
| 3/23 | Sheafs and Presheafs, cont'd | 5.4,5.11 | |
| 3/28 | Cech Cohomology | 5.33 | PS #8 |
| 3/30 | De Rham Theorem (weak version) | 5.10-5.12, 5.28-5.30 GH p43-45top | |
| 4/4 | Free Resolutions and Cohomology | 5.18-5.25,5.27 5.31,5.32,5.34-5.38 |
PS #9 |
| 4/6 | De Rham Isomorphism Theorem | ||
| 4/11,13 | No Class | ||
| 4/18 | Hodge Decomposition Theorem | 6.1-6.3,6.7-6.14 | PS #10 |
| 4/20 | Elliptic Operators | 6.4-6.6,6.28,6.34-6.36 | |
| 4/25 | Applications of Elliptic Regularity | 6.8,6.31 | |
| 4/27 | Proof of Elliptic Regularity | 6.29,6.32,6.33 | |
| 5/2 | Cohomology of Non-Compact Manifolds | Spivak, pp363-371 | PS #11 |
| 5/4 | Review | ||
| 5/9 | Final Exam, 1-3:30pm | ||