MAT 531: Topology & Geometry, II

Stony Brook            Spring 2011


Final Exam: Info, Course Overview, S06 exam/solutions, S10 exam/solutions, S11 exam/solutions
Midterm: Info, S06 exam/solutions, S10 exam/solutions, S11 exam/solutions.

General information about the course (TA's OHs updated 02/04)

Notes for Lectures 1-7 (02/18 update: Sections 10,12 slightly expanded). This is likely the end of the notes.
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: W 9-10:30am in P-143, 10:30am-12noon in 3-111


Tentative Schedule and Homework Assignments

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

Date Topic Read Problem Set
2/1Smooth manifolds1.0-1.6; Notes 1,2 ps1; solutions
2/3Tangent vectors and differentials 1.12-1.24; Notes 3,4
2/8Submanifolds and Inverse Function Theorem1.27-1.36; Notes 5 ps2; solutions
2/10 Implicit Function Theorems1.37-1.40; Notes 6
2/15Vector bundles1.25,1.44,1.45; Notes 7-10 ps3; solutions
2/171.54-1.59,2.1-2.13,4.1; Notes 10-12
2/22Vector fields1.41-1.43,1.46-1.50,1.53 ps4; solutions
2/24Frobenius Theorem1.51,1.52,1.54-1.64
3/1The differential2.14-2.23 ps5 solutions
3/3Frobenius Theorem (2nd version); Lie derivative2.26-2.32,2.24,2.25
3/8de Rham cohomology of Rn 4.13-4.15,4.18,4.19
ps6 solutions
3/10Integration on singular chains 4.6,4.7,4.16,4.17
3/15Integration on oriented manifolds 4.1-4.3,4.8-4.10; Notes 1-12
3/22no class b/c of midterm on Wednesday
3/23Midterm, 5-6:30pm, in Harriman 115
3/24(Co-)Chain complexes5.16,5.17 ps7 solutions
3/29Sheafs and presheafs 5.1-5.3,5.5-5.8
3/31Sheafs and presheafs, cont'd 5.4,5.11
4/5Cech Cohomology5.33 ps8 solutions
4/7de Rham Theorem (weak version) 5.10-5.12, 5.28-5.30
GH p43-45top
4/12Free resolutions and cohomology 5.18-5.25,5.27
ps9 solutions
4/14de Rham Isomorphism Theorem
4/19,21No Class
4/26Hodge Decomposition Theorem6.1-6.3,6.7-6.14 ps10 solutions
4/28Elliptic operators 6.4-6.6,6.28,6.34-6.36
5/3Applications of elliptic regularity6.8,6.31
5/5Proof of elliptic regularity 6.29,6.32,6.33 ps11 solutions
5/10Cohomology of non-compact manifolds Spivak, pp363-371
5/22Final Exam, 1-3:30pm, Math P-131

This page is maintained by Aleksey Zinger.
Last modified: May 22, 2011.