Math 102
Foundations of Smooth Manifolds
Fall 2011
Assignment 3
Due October 19, 2011
1. Boothby IV.2.10
2. Boothby IV.3.6
3. Boothby IV.3.8
4. Boothby IV.3.9
5. Let F : R3 R4 be given by F (x, y, z ) = (x2 y 2 , xy, xz, yz ) and let S 2 R3 be the unit sph
Math 102
Foundations of Smooth Manifolds
Fall 2011
Assignment 2 (Revised Oct. 7)
Due October 12, 2011
1. (Lee 1-6) By identifying R2 with C in the usual way, we can think of the unit circle as a subset of the
complex plane. An angle function on a subset U
Math 102
Foundations of Smooth Manifolds
Fall 2011
Assignment 1
Due October 5, 2011
Part A: Boothby Chp. III: 1.1, 1.3, 2.2, 2.3, 2.9, 3.3, 3.4 & 3.6
Part B:
1. Let V be an n-dimensional real vector space and let Aut(V ) be the space of all linear isomo
Math 102
Foundations of Smooth Manifolds
Fall 2011
Assignment 6
Due December 7, 2011
1. Lee 12-2
2. Lee 12-6
3. Lee 13-5
4. Lee 13-8
5. Lee 14-1
6. Lee 14-7
7. Lee 14-8
8. Lee 14-9
1
Math 102
Foundations of Smooth Manifolds
Fall 2011
Assignment 5
Due November 21, 2011
1. (Lee 19-7) Let U = cfw_(x1 , x2 , x3 ) R3 : xi > 0 now let X = x2 x3 x3 x2 and Y = x3 x1 x1 x3 .
The vector elds X and Y determine a smooth involutive 2-plane distrib
Math 102
Foundations of Smooth Manifolds
Fall 2011
Assignment 4
Due November 4, 2011
1. Let F : N M1 M2 given by F (p) = (f1 (p), f2 (p) be a smooth map. Show that for any p N
F : Tp N TF (p) M1 M2 Tf1 (p) N1 Tf2 (p) N2 is given by F (X ) = (f1 (X ), f2 (