MAT 566: Differential Topology

Stony Brook            Spring 2015

 

Announcements

Starting Wednesday, February 4, the class will be held in Physics P-125. Here is general information about the course.

References

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: Tu 9-12

 

Tentative Schedule

Problem Set 4 is due on Thursday, March 26, by 5pm, in 3-111

Date Topic Read Problem Set
01/26, Msnow day
01/28, W Review/overview of vector bundles Sections 1-3; VB Notes ps1
02/02, Msnow day
02/04, W Review of (co)homology
(Co)homology of manifolds
Munkres: Sections 31,33
Appendix A: pp257-260, 263bot-270
Appendix A: pp270-279
02/09, MStiefel-Whitney classes Section 4: pp37-50ps2
02/11, WStiefel-Whitney classes and cobordism
Grassmannians
Section 4: pp50-53
Section 5: pp55-62; G&H: pp193-194,207
02/16, MGrassmannians and vector bundlesSection 5: pp62-70
02/18, W(Co)homology of CW-complexes Sect. 6: pp73-74; App. A: pp260bot-263
02/23, M(Co)homology of Grassmannians Sections 6,7; G&H: pp194-197
02/25, WSchubert Calculus G&H: pp197-206; Vakil's slides 
03/02, MThom Isomorphism Theorem
Spanier pp255-263; Munkres: pp279-280
Sections 8,10; App. A: pp265bot-268top
ps3
03/04, W
03/09, MEuler classSection 9ps4
03/11, WTopology of smooth manifoldsSection 11
03/16, M Spring Break
03/18, W
03/23, MTopology of smooth manifolds (cont'd)Section 11
03/25, WChern Classes Section 12: pp143bot-146
Sections 13,14
ps5
03/30, M
04/01, WPontrjagin classesSection 15 
04/06, M Workshop on Birational Geometry
04/08, W
04/13, MChern and Pontrjagin numbersSection 16: pp183-193 
04/15, WApplications to oriented cobordism ring Section 16: pp190-195; Section 17 
04/20,MSome homotopy theory Spainer: Sections 7.2-7.5
Section 18
 
04/22, WThom-Pontrjagin construction 
04/27, MMultiplicative sequences Section 19: pp219-226
Warner: Chapter 6
 
04/29, WHirzebruch's Signature Theorem 
05/04, MAtiyah-Singer Index Theorem Spin Geometry: Chapter III 
05/06, WExotic smooth structures on S7Milnor's paper 
 

This page is maintained by Aleksey Zinger.
Last modified: March 25, 2015.