## MAT 531: Topology & Geometry, II

### Announcements

The final exam has been graded. If you are unable to stop by my office today (05/10), you can take a look at your exam on Wednesday or Friday of next week (05/17,19).

### Handouts

Notes on Vector Bundles, Course Overview
Detailed solutions to: final exam,midterm
From last year:
homework assignments, course summary, midterm, and final exam, prepared by Vladlen Timorin.

### Course Instructor

Name: Aleksey Zinger     E-mail: azinger@math     Phone: 432-8618
Office: Math Tower 3-117     Office Hours: Wed 9-12

### Schedule and Homework Assignments

 Date Topic Read Problem Set 1/24 Smooth Manifolds 1.1-1.6 PS #1 1/26 Partitions of Unity, Tangent Vectors 1.7-1.18 1/31 Tangent Bundle, Submanifolds 1.19-1.25,1.27-1.30 PS #2 2/2 Inverse Function Theorem 1.30-1.36 2/7 Implicit Function Theorems 1.37-1.43 PS #3 2/9 Vector Fields 1.44-1.53 2/14 Frobenius Theorem 1.54-1.64 PS #4 2/16 Differential Forms 2.1-2.18 2/21 The Differential 2.14-2.23 PS #5 2/23 Lie Derivative 2.24-2.32 2/28 de Rham Cohomology of Rn 4.13-4.15,4.18,4.194.4-4.6 PS #6 3/2 Integration on Singular Chains 4.6,4.7,4.16,4.174.1-4.3 3/7 Integration on Oriented Manifolds 4.1-4.3,4.8-4.10 3/9 Review 3/14 Midterm 3/16 (Co-)Chain Complexes 5.16,5.17 PS #7 3/21 Sheafs and Presheafs 5.1-5.3,5.5-5.8 3/23 Sheafs and Presheafs, cont'd 5.4,5.11 3/28 Cech Cohomology 5.33 PS #8 3/30 De Rham Theorem (weak version) 5.10-5.12, 5.28-5.30 GH p43-45top 4/4 Free Resolutions and Cohomology 5.18-5.25,5.275.31,5.32,5.34-5.38 PS #9 4/6 De Rham Isomorphism Theorem 4/11,13 No Class 4/18 Hodge Decomposition Theorem 6.1-6.3,6.7-6.14 PS #10 4/20 Elliptic Operators 6.4-6.6,6.28,6.34-6.36 4/25 Applications of Elliptic Regularity 6.8,6.31 4/27 Proof of Elliptic Regularity 6.29,6.32,6.33 5/2 Cohomology of Non-Compact Manifolds Spivak, pp363-371 PS #11 5/4 Review 5/9 Final Exam, 1-3:30pm