## MAT 566: Differential Topology
## Stony Brook Spring 2015 |
---|

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

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*

*Name:*
Aleksey Zinger
*E-mail:* azinger@math
*Phone:* 432-8618

*Office:* Math Tower 3-117
*Office Hours:* Tu 9-12

*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 | |||

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 | |||

04/01, W | Pontrjagin classes | Section 15 | |

04/06, M | Workshop on Birational Geometry | ||

04/08, W | |||

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 | ||

04/27, M | Multiplicative sequences | Section 19: pp219-226 Warner: Chapter 6 | |

04/29, W | Hirzebruch's Signature Theorem | ||

05/04, M | Atiyah-Singer Index Theorem | Spin Geometry: Chapter III | |

05/06, W | Exotic smooth structures on S^{7} | Milnor's paper |

This page is maintained by Aleksey Zinger.