| Week #1 |
- Manifolds, tangent space, derivatives, induced map. (M 1, GP 1.2);
- Inverse function theorem and immersions. (M 1, GP 1.3);
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April 2nd: classes begin |
| Week #2 |
- Immersion, Submersions (GP 1.4);
- Regular values (M 2);
- Transversality (GP 1.5)
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| Week #3 |
- Fundamental Theorem of Algebra. (M 2)
- Homotopy and stability. (GP 1.6)
- Sard thorem and Morse functions. (GP 1.7, M 2)
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April 20th: Last day to add or drop a class;
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| Week #4 |
- Manifolds with boundary (GP 2.1, M, p12)
- Brower fixed point theorem (M, p13, GP 2.2)
- Proof of Sard and Morse functions (M 3, GP 1.7)
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| Week #5 |
- Transversality and intersection. Epsilon-neighborhood theorem. (GP 2.3).
- Smooth homotopy (GP 1.6, M9)
- Degree modula 2 (GP 2.4, M8);
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| Week #6 |
- Winding number (GP 2.5)
- Jordan-Brouwer separation theorem.
- Borsuk Ulam theorem (GP 2.6)
- Orientation (GP 3.1,2 M10)
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| Week #7 |
- Oriented intersection number (GP 3.3)
- Lefschetz fixed point theorem (GP 3.4)
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May 14th: Term withdrawal deadline. |
| Week #8 |
- Vector fields and Poincare-Hopf Theorem (GP 3.5)
- Euler Characteristic and Triangulations (GP 3.7, M6).
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May 25th: Change of grading basis deadline.
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| Week #9 |
- Framed cobordism and Pontriagin construction (M7)
- Hopf degree theorem (GP 3.6)
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May 28th: Memorial Day
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| Week #10 |
- Whitney embedding theorem (GP 1.8)
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June 1-6: End-Quarter Period. |
| Final Exam |
June 9th: 8:30-11:30 |
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