MAT 531: Topology & Geometry, II

Stony Brook            Spring 2010



Final Exam: Info, Course Overview, Spring 06 exam and solutions, Spring 10 exam and solutions
Midterm: Info, Spring 06 exam and solutions, Spring 10 exam and solutions

General information about the course (TA's OHs updated 01/26)

Notes on Vector Bundles

Notes on Lectures 1-5
Bonus: 1 HW pt for each typo you find, 3pts for minor error, 5pts for significant error, 10pts for very significant error (only 1 bonus per typo/error, to the first person who let's me know; the points will be added to your problem set scores)


Course Instructor

Name: Aleksey Zinger     E-mail: azinger@math     Phone: 432-8288
Office: Math Tower 3-111     Office Hours: Tu 2:20-3:50pm, W 9-10:30am in P-143


Tentative Schedule and Homework Assignments

Please read the assigned sections from the book before the corresponding lecture.

Date Topic Read Problem Set
1/26Smooth manifolds1.0-1.6 ps1
1/28Tangent vectors and differentials 1.12-1.24
2/2Vector bundles 1.25; Notes 1-3 ps2
2/4Submanifolds and Inverse Function Theorem1.27-1.36; Notes 4.1-4.4
2/9Implicit Function Theorems1.37-1.40 ps3
2/11Vector fields1.41-1.43,1.46-1.50,1.53
2/16Frobenius Theorem1.44,1.45,1.51,1.52,1.54-1.61 ps4
2/18Integral submanifolds; some algebra 1.62-1.64,2.1-2.13
2/23The differential2.14-2.23 ps5
2/25Frobenius Theorem (2nd version); Lie derivative2.26-2.32,2.24,2.25
3/2de Rham cohomology of Rn 4.13-4.15,4.18,4.19
3/4Integration on singular chains 4.6,4.7,4.16,4.17
3/9Integration on oriented manifolds 4.1-4.3,4.8-4.10; Notes 4-6
3/16no class b/c of midterm W
3/17Midterm: 5-6:20pm
3/18(Co-)Chain complexes5.16,5.17 ps7
3/23Sheafs and presheafs 5.1-5.3,5.5-5.8
3/25Sheafs and presheafs, cont'd 5.4,5.11
3/30,4/1No Class
4/6Cech Cohomology5.33 ps8
4/8De Rham Theorem (weak version) 5.10-5.12, 5.28-5.30
GH p43-45top
4/13Free resolutions and cohomology 5.18-5.25,5.27
4/15De Rham Isomorphism Theorem
4/20Hodge Decomposition Theorem6.1-6.3,6.7-6.14 ps10
4/22Elliptic operators 6.4-6.6,6.28,6.34-6.36
4/27Applications of elliptic regularity6.8,6.31
4/29Proof of elliptic regularity 6.29,6.32,6.33 ps11
5/4Cohomology of non-compact manifolds Spivak, pp363-371
5/16Final Exam, 12:30-3pm

This page is maintained by Aleksey Zinger.
Last modified: May 17, 2010.