MAT 531: Topology & Geometry, II

Stony Brook            Spring 2006



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).



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
1/24Smooth Manifolds1.1-1.6 PS #1
1/26Partitions of Unity, Tangent Vectors 1.7-1.18
1/31Tangent Bundle, Submanifolds 1.19-1.25,1.27-1.30 PS #2
2/2Inverse Function Theorem1.30-1.36
2/7Implicit Function Theorems1.37-1.43 PS #3
2/9Vector Fields1.44-1.53
2/14Frobenius Theorem1.54-1.64 PS #4
2/16Differential Forms2.1-2.18
2/21The Differential2.14-2.23 PS #5
2/23Lie Derivative2.24-2.32
2/28de Rham Cohomology of Rn 4.13-4.15,4.18,4.19
PS #6
3/2Integration on Singular Chains 4.6,4.7,4.16,4.17
3/7Integration on Oriented Manifolds 4.1-4.3,4.8-4.10
3/16(Co-)Chain Complexes5.16,5.17 PS #7
3/21Sheafs and Presheafs 5.1-5.3,5.5-5.8
3/23Sheafs and Presheafs, cont'd 5.4,5.11
3/28Cech Cohomology5.33 PS #8
3/30De Rham Theorem (weak version) 5.10-5.12, 5.28-5.30
GH p43-45top
4/4Free Resolutions and Cohomology 5.18-5.25,5.27
PS #9
4/6De Rham Isomorphism Theorem
4/11,13No Class
4/18Hodge Decomposition Theorem6.1-6.3,6.7-6.14 PS #10
4/20Elliptic Operators 6.4-6.6,6.28,6.34-6.36
4/25Applications of Elliptic Regularity6.8,6.31
4/27Proof of Elliptic Regularity 6.29,6.32,6.33
5/2Cohomology of Non-Compact Manifolds Spivak, pp363-371PS #11
5/9Final Exam, 1-3:30pm

This page is maintained by Aleksey Zinger.
Last modified: July 25, 2009.