MAT 566: Differential Topology
Stony Brook            Spring 2018 |
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All readings listed in the table below are from Milnor&Stasheff's Characteristic Classes, except
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Date | Topic | Read | Problem Set |
01/23, Tu | Review/overview of vector bundles | Sections 1-3; VB Notes | ps1 |
01/25, Th | Review of (co)homology | Munkres: Sections 31,33 Appendix A: pp257-260, 263bot-270 | |
02/06, Tu | Poincare Duality | Appendix A: pp270-279 | |
02/08, Th | Stiefel-Whitney classes | Section 4: pp37-50 | ps2 |
02/13, Tu | Stiefel-Whitney classes and cobordism Grassmannians |
Section 4: pp50-53 Section 5: pp55-62; G&H: pp193-194,207 | |
02/15, Th | Grassmannians and vector bundles | Section 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, Tu | Schubert Calculus | G&H: pp197-206; Vakil's slides | ps3 |
03/01, Th | Thom Isomorphism Theorem |
Spanier pp255-263; Munkres: pp279-280 Sections 8,10; App. A: pp265bot-268top | |
03/06, Tu | Applications of TI | Section 9 | ps4 |
03/06, Tu | Euler class | ||
03/20, Tu | Topology of smooth manifolds | Section 11 | |
03/22, Th | |||
03/27, Tu | Chern classes | Section 12: pp143bot-146 Sections 13,14 |
ps5 |
03/29, Th | |||
04/03, Tu | |||
04/05, Th | Atiyah-Bott Localization Theorem |
Atiyah-Bott's paper: Sections 2,3 Notes on Mirror Symmetry: Chapter 1 | |
04/10, Tu | Pontrjagin classes | Section 15 | ps6 |
04/12, Th | Chern and Pontrjagin numbers | Section 16: pp183-193 | |
04/17, Tu | Oriented cobordism ring | Section 16: pp190-195; Section 17 | |
04/19, Th | Thom-Pontrjagin construction Some homotopy theory |
Section 18 Spainer: Sections 7.2-7.5 |
ps7 |
04/24, Tu | Thom-Multiplicative sequences | Section 19 | |
04/26, Th | Hirzebruch Signature Theorem | ||
05/01, Tu | Exotic smooth structures on S7 | Milnor's paper | none |
05/03, Th | Atiyah-Singer Index Theorem | Spin Geometry: Chapter III |
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