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
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A first course in Differential Geometry, covering: Vector bundles -including the tangent bundle, vector fields, differential forms, Riemannian metrics, symplectic structures, and a general discussion of tensors, and connections from a variety of viewpoints. Depending on time and the sophistication of the audience we will proceed to more advanced subjects. For example a discussion of the h-principle and its role in differential geometry.
Lecturer
- Joseph Coffey
- coffey@math.stanford.edu 381N 646-234-6840 Office hours: Mon 3-4, Wed 3-4
Course texts
Grading Policy
- 60% Weekly Homework sets - Drop Lowest 2
- 40 % Final Exam
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