MAT 566, Spring 2015

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

Munkres: Munkres, Elements of Algebraic Topology
G&H: Griffiths&Harris, Principles of Algebraic Geometry
Vakil's slides: Vakil, slides for 2005 MAA Inivited Address
Spanier: Spanier, Algebraic Topology
Atiyah-Bott: Atiyah&Bott, The Moment Map and Equivariant Cohomology, Topology 1984
Mirror Symmetry: K. Hori, et. al., Mirror Symmetry
Milnor's paper: Milnor, On manifolds homeomorphic to the 7-sphere, Annals of Math, 1956
Warner: Warner, Foundations of Differentiable Manifolds and Lie Groups
Spin Geometry: Lawson&Michelsohn, Spin Geometry

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, M	snow day
01/28, W	Review/overview of vector bundles	Sections 1-3; VB Notes	ps1
02/02, M	snow 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, M	Stiefel-Whitney classes	Section 4: pp37-50	ps2
02/11, W	Stiefel-Whitney classes and cobordism Grassmannians	Section 4: pp50-53 Section 5: pp55-62; G&H: pp193-194,207
02/16, M	Grassmannians and vector bundles	Section 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, W	Schubert Calculus	G&H: pp197-206; Vakil's slides
03/02, M	Thom Isomorphism Theorem	Spanier pp255-263; Munkres: pp279-280 Sections 8,10; App. A: pp265bot-268top	ps3
03/04, W	Thom Isomorphism Theorem		ps3
03/09, M	Euler class	Section 9	ps4
03/11, W	Topology of smooth manifolds	Section 11
03/16, M	Spring Break
03/18, W
03/23, M	Topology of smooth manifolds (cont'd)	Section 11
03/25, W	Chern Classes	Section 12: pp143bot-146 Sections 13,14	ps5
03/30, M	Chern Classes	Section 12: pp143bot-146 Sections 13,14	ps5
04/01, W	Pontrjagin classes	Section 15
04/06, M	Workshop on Birational Geometry
04/08, W	Workshop on Birational Geometry
04/13, M	Chern and Pontrjagin numbers	Section 16: pp183-193
04/15, W	Applications to oriented cobordism ring	Section 16: pp190-195; Section 17
04/20,M	Some homotopy theory	Spainer: Sections 7.2-7.5 Section 18
04/22, W	Thom-Pontrjagin construction	Spainer: Sections 7.2-7.5 Section 18
04/27, M	Multiplicative sequences	Section 19: pp219-226 Warner: Chapter 6
04/29, W	Hirzebruch's Signature Theorem	Section 19: pp219-226 Warner: Chapter 6
05/04, M	Atiyah-Singer Index Theorem	Spin Geometry: Chapter III
05/06, W	Exotic smooth structures on S⁷	Milnor's paper

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