## MAT 531: Topology & Geometry, II
## Stony Brook Spring 2010 |
---|

**Final Exam:**
Info,
Course Overview,
Spring 06 exam
and solutions,
Spring 10 exam
and solutions

**Midterm:**
Info,
Spring 06 exam
and solutions,
Spring 10 exam
and solutions

General information about the course (TA's OHs updated 01/26)

Notes on Lectures 1-5

**Bonus:** 1 HW pt for each typo you find,
3pts for minor error,
5pts for significant error, 10pts for very significant error
(only 1 bonus per typo/error, to the first person who let's me know;
the points will be added to your problem set scores)

*Name:*
Aleksey Zinger
*E-mail:* azinger@math
*Phone:* 432-8288

*Office:* Math Tower 3-111
*Office Hours:* Tu 2:20-3:50pm, W 9-10:30am in P-143

Date |
Topic |
Read |
Problem Set |

1/26 | Smooth manifolds | 1.0-1.6 | ps1 |

1/28 | Tangent vectors and differentials | 1.12-1.24 | |

2/2 | Vector bundles | 1.25; Notes 1-3 | ps2 |

2/4 | Submanifolds and Inverse Function Theorem | 1.27-1.36; Notes 4.1-4.4 | |

2/9 | Implicit Function Theorems | 1.37-1.40 | ps3 |

2/11 | Vector fields | 1.41-1.43,1.46-1.50,1.53 | |

2/16 | Frobenius Theorem | 1.44,1.45,1.51,1.52,1.54-1.61 | ps4 |

2/18 | Integral submanifolds; some algebra | 1.62-1.64,2.1-2.13 | |

2/23 | The differential | 2.14-2.23 | ps5 |

2/25 | Frobenius Theorem (2nd version); Lie derivative | 2.26-2.32,2.24,2.25 | |

3/2 | de Rham cohomology of R^{n} |
4.13-4.15,4.18,4.19 4.4-4.6 |
ps6 |

3/4 | Integration on singular chains | 4.6,4.7,4.16,4.17 | |

3/9 | Integration on oriented manifolds | 4.1-4.3,4.8-4.10; Notes 4-6 | |

3/11 | Review | ||

3/16 | no class b/c of midterm W | ||

3/17 | Midterm: 5-6:20pm | ||

3/18 | (Co-)Chain complexes | 5.16,5.17 | ps7 |

3/23 | Sheafs and presheafs | 5.1-5.3,5.5-5.8 | |

3/25 | Sheafs and presheafs, cont'd | 5.4,5.11 | |

3/30,4/1 | No Class | ||

4/6 | Cech Cohomology | 5.33 | ps8 |

4/8 | De Rham Theorem (weak version) | 5.10-5.12, 5.28-5.30 GH p43-45top | |

4/13 | Free resolutions and cohomology | 5.18-5.25,5.27 5.31,5.32,5.34-5.38 |
ps9 |

4/15 | De Rham Isomorphism Theorem | ||

4/20 | Hodge Decomposition Theorem | 6.1-6.3,6.7-6.14 | ps10 |

4/22 | Elliptic operators | 6.4-6.6,6.28,6.34-6.36 | |

4/27 | Applications of elliptic regularity | 6.8,6.31 | |

4/29 | Proof of elliptic regularity | 6.29,6.32,6.33 | ps11 |

5/4 | Cohomology of non-compact manifolds | Spivak, pp363-371 | |

5/6 | Review | ||

5/16 | Final Exam, 12:30-3pm |

This page is maintained by Aleksey Zinger.