MAT 566: Differential Topology

Stony Brook            Fall 2006



Problem Set 7 is due on Thursday, December 14, by 5pm, in Math 3-117.

Here are some Notes on the Splitting Principle.

Here is general information about the course (revised 9/7).


All readings listed in the table below are from Milnor&Stasheff's Characteristic Classes, except


Course Instructor

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



Problem Set 7 is due on Thursday, December 14, by 5pm, in Math 3-117

Date Topic Read Problem Set
9/7Review of Vector BundlesSections 1-3 pdf, ps
9/12 Review/Overview of (Co)homology Munkres: Chap 7; Sects 31,33
App. A: pp257-260, 263bot-266, 268
9/19(Co)homology of Manifolds Appendix A: pp270-279
9/21Applications of Stiefel-Whitney Classes Section 4: pp37-50
9/26Stiefel-Whitney Classes and Cobordism
Section 4: pp50-53
Section 5: pp55-62; G&H: pp193-194,207
pdf, ps
9/28 Grassmannians and Vector Bundles Section 5: pp62-70
10/3(Co)homology of CW-Compelexes Sect. 6: pp73-74; App. A: pp260bot-263
10/5(Co)homology of Grassmannians Sections 6,7; G&H: pp194-197
10/10Schubert Calculus (by Paul and Ritwik)G&H: pp197-206; Vakil's slides 
10/12Thom Isomorphism Theorem
Spanier pp255-263; Munkres: pp279-280
Sections 8,10; App. A: pp265bot-268top
pdf, ps
10/19Euler ClassSection 9 pdf, ps
10/24Topology of Smooth Manifolds Section 11
10/31Chern Classes Section 12: pp143bot-146
Sections 13,14
pdf, ps
11/7Enumerative Geometry of Plane Curves
(by Caner and Chris)
expository notes
11/9Atiyah-Bott Localization Theorem
(by Robert F. and Thomas)
Atiyah-Bott's paper: Sections 2,3
Mirror Symmetry: Sections 4.1-4.3
11/14Pontrjagin ClassesSection 15 pdf, ps
11/16Chern and Pontrjagin NumbersSection 16: pp183-193
11/21Applications to Oriented Cobordism Ring Section 16: pp190-195; Section 17
11/28Some Homotopy Theory Spainer: Sections 7.2-7.5
Section 18
pdf, ps
11/30Thom-Pontrjagin Construction
12/5Multiplicative Sequences Section 19: pp219-226
Warner: Chapter 6
12/7Hirzebruch's Signature Theorem
12/12Exotic Smooth Structures on S7 Milnor's paper 
12/14Atiyah-Singer Index Theorem Spin Geometry: Chapter III 

This page is maintained by Aleksey Zinger.
Last modified: December 2, 2006.