## 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

- 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*

*Problem Set 1 is due on Monday, 2/12, by 5pm, in Math 3-111*

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, W | Schubert Calculus | G&H: pp197-206; Vakil's slides |

This page is maintained by Aleksey Zinger.