Evans 3, Tuesdays and Thursdays from 9:30-11.00 AM

Mondays 9:40-11.10am, Evans Hall 859

In case you have any quastions please come see me.

If Monday does not work, please email me and ask for appointment for other time.

I assume the knowledge of the following concepts from calculus and point-set topology:

1 Continuity, differentiability, smoothness for functions from R^n to R^m

2 Topology: open and closed sets, compactness, covers, homeomorphisms.

Suggested reading: A. Hatcher's Notes on introductory point-set topology

The textbook for this course is *Differential Topology *by Guillemin and Pollack.

Milnor, *Topology From the Differentiable Viewpoint*

**Grading**: 30% Homework, 30% Midterms, 40% Final.

There will be one homework every one or two weeks. They will be posted on this page together with the due date. Late homework will not be accepted under any circumstance. However, your two lowest homework grades will not be included in the final grade calculation. Discussing of the problems with other students is encouraged.

There will be one midterm exam on October 4. The midterm will be in class. The final exam is Tuesday December 13 at Evans 3 from 3-6 pm. In the case of a fire alarm during either of the midterms or the final exam, leave your exams in the room, face down, before evacuating. Under no circumstances should you take the exam with you.

If you have a documented disability and require special accommodations of any kind, please e-mail me as soon as possible, and no later than September 13.

# | Date | Topic | Readings | Hw | Notes |

1 | 8/25 | Introduction, point-set topology | Point-set topology | ||

2 | 8/30 | Smooth manifolds, smooth maps | 1.1 | ||

3 | 9/1 | Derivatives, tangent spaces | 1.2 | HW1 Out | |

4 | 9/6 | Immesrions |
1.3 | ||

5 | 9/8 | Submersions | 1.4 | HW2 Out HW1 Due | |

6 | 9/13 | Transversality | 1.5 | ||

7 | 9/15 | Sard's theorem | 1.6, 1.7 | ||

8 | 9/20 | Embedding of manifolds to Euclidian space | 1.8 | HW3 Out HW 2 Due | |

9 | 9/22 | Embedding of manifolds to Euclidian space 2 | 1.8 | ||

10 | 9/27 | Overview of chapter 1 | Chapter 1 | HW4 Out | |

11 | 9/29 | Overview of chapter 1, Problem solving | Chapter 1 | HW3 Due | |

12 | 10/4 | Midterm | The midterm cover topics Ch.1 | ||

13 | 10/6 | Manifolds with boundary | 2.1 | HW4 Out | |

14 | 10/11 | One Manifolds | 2.2 | ||

15 | 10/13 | One Manifolds 2 | 2.2 | ||

16 | 10/18 | Transversality | 2.3 | HW 4 Due | |

17 | 10/20 | Transversality | 2.3 | HW5 Out | |

18 | 10/25 | Intersection theory mod 2 | 2.4 | ||

19 | 10/27 | Intersection theory mod 2 | 2.4 | HW5 Due | |

20 | 11/1 | Winding Numbers | 2.5 | ||

21 | 11/3 | The Borsuk-Ulam theorem | 2.6 | HW6 Out | |

22 | 11/8 | The Borsuk-Ulam theorem | 2.6 | ||

23 | 11/10 | Integration on manifolds | 4.1 | HW6 Due | |

24 | 11/15 | Exteriour algebra | 4.2 | HW7 Out | |

25 | 11/17 | Differential forms | 4.3 | ||

26 | 11/22 | Integration | 4.4 | HW7 Due, HW8 Out | |

27 | 11/24 | No class, academic holiday | |||

28 | 11/29 | Exteriour derivative | 4.5 | ||

29 | 12/1 | Cohomology | 4.5-4.6 | ||

30 | 12/6 | Cohomology | 4.6 | ||

31 | 12/13 | Final exam 3pm-6pm |