Instructor:  Paul Feehan

Math Tower 632
(614) 292-8678
feehan@math.ohio-state.edu
http://www.math.ohio-state.edu/~feehan

Office Hours:

MWF 10:30 - 11:20  and  F 8:30-9:20 or by appointment.

Makeup Schedule
Homework Problems
Reference Articles

Makeup Schedule:

Monday,    Oct 11: class as usual in JR139, 3:30-5:15pm (extra 30min)

Wednesday, Oct 13: no class
Monday,        Oct 18: no class
Wednesday, Oct 20:no class

Makeup classes and extended periods:

Friday,            Oct 22: makeup in JR139 (or MW154), 3:30-4:30pm (extra 60min)
Monday,        Oct 25: class as usual in JR139, 3:30-5:15pm                 (extra 30min)
Wednesday,  Oct 27: class as usual in JR139, 3:30-5:15pm                (extra 30min)
Friday,            Oct 29: makeup in JR139 (or MW154), 3:30-4:30pm (extra 60min)
Monday,        Nov  1: class as usual in JR139, 3:30-5:15pm                 (extra 30min)
Friday,            Nov 5: makeup in JR139 (or MW154), 3:30-4:20pm  (extra 45min)

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Homework Problems:

Unless noted otherwise, these problems are all taken from Guillemin and Pollack.

Week of 9/20

Section 1.1: 6, 11, 12
Section 1.2: 12

Week of 9/27

Section 1.3: 3, 4, 7, 10
Section 1.4: 1, 2, 5, 8, 10, 11, 12
Section 1.5:  2, 4, 5, 6, 7, 10

Week of 10/4

Section 1.6: 3, 9, 10, 11
Section 1.7: 10, 11, 12, 14, 15, 17, 18
Section 1.8:  6, 7, 8, 10. Read proof of "non-compact" Whitney embedding theorem, pp. 53-54.

Week of 10/11

Section 2.1: 1, 2, 3, 6, 7, 8, 9, 10, 11
Section 2.2: 1, 2, 3, 4
Section 2.3: 1, 2, 3, 4, 5, 6, 10, 11, 12, 13, 16

Week of 10/18

Section 2.4: 1, 3, 7, 10, 12, 14, 15, 16, 17, 19

Week of 10/25

Section 2.5: All problems

Week of 11/1

Section 3.2: 3, 4, 7, 9, 14, 17, 18, 19, 20, 26

Week of 11/8

Section 3.3: 1, 2, 3, 9, 12, 14, 15, 17

Week of 11/15

Section 3.4: 3, 6, 7, 9, 10, 11

Weeks of 11/22 and 12/1

Section 3.5: 1-19

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Reference Articles:

• Donaldson, S. K.  AMS MathSciNet Bibliography .
• Donaldson, S. K. Irrationality and the $h$-cobordism conjecture. J. Differential Geom. 26 (1987), 141-168.
• Milnor, J.  AMS MathSciNet Bibliography .
• Milnor, J. Lectures on the $h$-cobordism theorem. Notes by L. Siebenmann and J. Sondow. Princeton University Press, Princeton, N.J. 1965.
• Milnor, J. On manifolds homeomorphic to the $7$-sphere. Ann. of Math. (2) 64 (1956), 399-405.  [ ps, pdf ]
• Nash, J.   AMS MathSciNet Bibliography .
• Nash, J. The imbedding problem for Riemannian manifolds. Ann. of Math. (2) 63 (1956), 20-63.  [ps,pdf ]
• Smale, S.  AMS MathSciNet Bibliography.
• Smale, S. An infinite dimensional version of Sard's theorem. Amer. J. Math. 87 (1965) 861-866.
• Smale, S. On the structure of manifolds. Amer. J. Math. 84 (1962) 387-399.
• Smale, S. Generalized Poincaré's conjecture in dimensions greater than four. Ann. of Math. (2) 74 (1961) 391-406.  [ps,  pdf ]
• Whitney, H.  AMS MathSciNet Bibliography.
• Whitney, H. The singularities of a smooth $n$-manifold in $2n$-space. Ann. of Math. (2) 45, (1944) 220-246. [ps , pdf ]

 

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Paul M. N. Feehan
Department of Mathematics
Ohio State University
231 West 18th Avenue
Columbus, OH 43210
(614) 292-8678