MAT 566: Differential Topology

Stony Brook            Spring 2018

 

General Course Information, A Proof and a Modern ``Proof"

References

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

 

Tentative Schedule

Problem Set 5 is due on Monday, 04/09, by 5pm, in Math 3-111

Date Topic Read Problem Set
01/23, TuReview/overview of vector bundles Sections 1-3; VB Notes ps1
01/25, ThReview of (co)homology Munkres: Sections 31,33
Appendix A: pp257-260, 263bot-270
02/06, TuPoincare Duality Appendix A: pp270-279
02/08, ThStiefel-Whitney classes Section 4: pp37-50ps2
02/13, TuStiefel-Whitney classes and cobordism
Grassmannians
Section 4: pp50-53
Section 5: pp55-62; G&H: pp193-194,207
02/15, ThGrassmannians and vector bundlesSection 5: pp62-70
02/20, Tu(Co)homology of CW-complexes Sect. 6: pp73-74; App. A: pp260bot-263
02/22, Th(Co)homology of Grassmannians Sections 6,7; G&H: pp194-197
02/27, TuSchubert Calculus G&H: pp197-206; Vakil's slides ps3
03/01, ThThom Isomorphism Theorem
Spanier pp255-263; Munkres: pp279-280
Sections 8,10; App. A: pp265bot-268top
03/06, TuApplications of TISection 9 ps4
03/06, TuEuler class
03/20, TuTopology of smooth manifolds Section 11
03/22, Th
03/27, TuChern classes Section 12: pp143bot-146
Sections 13,14
ps5
03/29, Th
04/03, Tu
04/05, ThAtiyah-Bott Localization Theorem
Atiyah-Bott's paper: Sections 2,3
Notes on Mirror Symmetry: Chapter 1
04/10, TuPontrjagin classesSection 15 ps6
04/12, ThChern and Pontrjagin numbersSection 16: pp183-193
04/17, TuOriented cobordism ring Section 16: pp190-195; Section 17
04/19, ThThom-Pontrjagin construction
Some homotopy theory
Section 18
Spainer: Sections 7.2-7.5
ps7
04/24, TuThom-Multiplicative sequencesSection 19
04/26, ThHirzebruch Signature Theorem
05/01, TuExotic smooth structures on S7 Milnor's papernone
05/03, ThAtiyah-Singer Index Theorem Spin Geometry: Chapter III
 

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Last modified: January 7, 2018.