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MAT 531: Topology & Geometry, II
Stony Brook Spring 2011 |
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Final Exam:
Info, Course Overview,
S06 exam/solutions,
S10 exam/solutions,
S11 exam/solutions
Midterm:
Info,
S06 exam/solutions,
S10 exam/solutions,
S11 exam/solutions.
General information about the course (TA's OHs updated 02/04)
Notes for Lectures 1-7
(02/18 update: Sections 10,12 slightly expanded). This is likely the end
of the notes.
Bonus: 1 HW pt for each typo you find,
3pts for minor error,
5pts for significant error, 10pts for very significant error
(only 1 bonus per typo/error, to the first person who let's me know;
the points will be added to your problem set scores)
Name:
Aleksey Zinger
E-mail: azinger@math
Phone: 432-8288
Office: Math Tower 3-111
Office Hours: W 9-10:30am in P-143, 10:30am-12noon in 3-111
| Date | Topic | Read | Problem Set |
| 2/1 | Smooth manifolds | 1.0-1.6; Notes 1,2 | ps1; solutions |
| 2/3 | Tangent vectors and differentials | 1.12-1.24; Notes 3,4 | |
| 2/8 | Submanifolds and Inverse Function Theorem | 1.27-1.36; Notes 5 | ps2; solutions |
| 2/10 | Implicit Function Theorems | 1.37-1.40; Notes 6 | |
| 2/15 | Vector bundles | 1.25,1.44,1.45; Notes 7-10 | ps3; solutions |
| 2/17 | 1.54-1.59,2.1-2.13,4.1; Notes 10-12 | ||
| 2/22 | Vector fields | 1.41-1.43,1.46-1.50,1.53 | ps4; solutions |
| 2/24 | Frobenius Theorem | 1.51,1.52,1.54-1.64 | |
| 3/1 | The differential | 2.14-2.23 | ps5 solutions |
| 3/3 | Frobenius Theorem (2nd version); Lie derivative | 2.26-2.32,2.24,2.25 | |
| 3/8 | de Rham cohomology of Rn | 4.13-4.15,4.18,4.19 4.4-4.6 |
ps6 solutions |
| 3/10 | Integration on singular chains | 4.6,4.7,4.16,4.17 | |
| 3/15 | Integration on oriented manifolds | 4.1-4.3,4.8-4.10; Notes 1-12 | |
| 3/17 | Review | ||
| 3/22 | no class b/c of midterm on Wednesday | ||
| 3/23 | Midterm, 5-6:30pm, in Harriman 115 | ||
| 3/24 | (Co-)Chain complexes | 5.16,5.17 | ps7 solutions |
| 3/29 | Sheafs and presheafs | 5.1-5.3,5.5-5.8 | |
| 3/31 | Sheafs and presheafs, cont'd | 5.4,5.11 | |
| 4/5 | Cech Cohomology | 5.33 | ps8 solutions |
| 4/7 | de Rham Theorem (weak version) | 5.10-5.12, 5.28-5.30 GH p43-45top | |
| 4/12 | Free resolutions and cohomology | 5.18-5.25,5.27 5.31,5.32,5.34-5.38 |
ps9 solutions |
| 4/14 | de Rham Isomorphism Theorem | ||
| 4/19,21 | No Class | ||
| 4/26 | Hodge Decomposition Theorem | 6.1-6.3,6.7-6.14 | ps10 solutions |
| 4/28 | Elliptic operators | 6.4-6.6,6.28,6.34-6.36 | |
| 5/3 | Applications of elliptic regularity | 6.8,6.31 | |
| 5/5 | Proof of elliptic regularity | 6.29,6.32,6.33 | ps11 solutions |
| 5/10 | Cohomology of non-compact manifolds | Spivak, pp363-371 | |
| 5/12 | Review | ||
| 5/22 | Final Exam, 1-3:30pm, Math P-131 | ||