WEEK |
BRIEF DESCRIPTION |
notes/homeworks/solutions |
before starting |
Refreshing topology (based on Munkres: Topology 2nd Ed.) Chap 41: locally-finite, paracompactness, normal/regular spaces; Chap 36: imbeddings of manifolds,
partition of unity;
Chap 50: dimension theory |
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01/12- 01/18 |
partition of unity |
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01/19- 01/25 |
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1.1 #3, 4, 11, 12; 1.2 # 4, 5 |
01/26- 02/1 |
Submersion theorem, preimage theorem, cutting out submanifolds |
1.2 #11; 1.3 # 2, 5, 10; 1.4 #2, 6, 7 |
02/2- 02/8 |
Transversality, stability and homotopy |
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02/9- 02/15 |
Sard's theorem, Whitney embedding theorem (Umich math 437W13 note, UToronto math 1300 note, an explicit construction of injective immersion is missing from Victor's book, should read these notes), Transversality (section 2.3) |
1.5 #6, 7, 9, 10; 1.6 #3, 7, 8 |
02/16- 02/22 |
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02/23- 03/01 |
transversality and Sard's for manifolds-with-boundary; Classification of compact one-manifolds, Brouwer fixed point theorem |
2.1 #2, 8, 10, 11; 2.2 #2, 3, 6, 7 |
03/02- 03/08 |
The transversality theorem |
2.3 #2,3,5,12,18,20 |
03/09- 03/15 |
Intersection theory Mod 2, Jordan-Brouwer separation theorem |
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