Chapter 5, #17
Chapter 6, #7
Chapter 7, # 6
Chapter 7, #11
Show that the distribution in R3 given by the equation:
d z - y d x = 0
is nowhere integrable.
Syllabus
- Week 1 - Definition of Manifold , Vector Bundles, Definition of Tangent Bundle, Tensors - Reading Vol 1Chapt 1,2,3
Tuesday, October 17, 2006
Wednesday, October 04, 2006
HW 1
Here is the homework assignment. It is due next Wed.
Chapt 2 (Vol 1) of Spivak 3,11
Show that if M is a smooth n manifold, and N is a smooth k-manifold, and f:M->N is a surjective, smooth map then there a set of full measure U in N, such that for each x in U, f^-1(x) is a smooth n-k manifold.
Show that a bundle E is orientable if and only if /\^n(E) admits a no where vanishing section. (The crazy asci mess there denote the highest wedge power of E). Show that E is orientable if and only if its dual is.
Chapter 3, number 27
Chapter 4 numbers 1,8
Chapt 2 (Vol 1) of Spivak 3,11
Show that if M is a smooth n manifold, and N is a smooth k-manifold, and f:M->N is a surjective, smooth map then there a set of full measure U in N, such that for each x in U, f^-1(x) is a smooth n-k manifold.
Show that a bundle E is orientable if and only if /\^n(E) admits a no where vanishing section. (The crazy asci mess there denote the highest wedge power of E). Show that E is orientable if and only if its dual is.
Chapter 3, number 27
Chapter 4 numbers 1,8
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