Introduction to the Geometry and Topology of Manifolds I (MAT 501), fall 2016


Homework assignment for this week: 

-Week 14: Read pp. 97-113 of Hatcher. Hand in problems 4,5,8 of p. 131 in class on 12/1.

-Week 12: Read pp. 68-78 of Hatcher. Hand in problems 12,14,25,27 of p. 80-82 in class on 11/22 (Bonus: #20).

-Week 10: Read pp. 56-68 of Hatcher. Hand in problems 3, 4, 5, 9, 10 of p. 79 in class on 11/3.

-Week 8: Read pp. 40-52 of Hatcher. Hand in problems 3,4,7,8,9,14 of pp. 52-54 in class on 10/20 (Bonus: #22). Office hours the week of Fall Break will be Wednesday, 10/12, 3-4 pm in WXLR 431.

-Week 6: Read pp. 1-4 and 31-37 of Hatcher. Hand in problems #5, 6 (a)&(b) of p. 18 (6(c) is optional) and 12, 16, 17 of p. 39 in class on 10/6. There will be no office hours on Tuesday 9/27, they will be on Monday 9/26 instead, 3-4 pm in WXLR 431.

-Week 4: Read pp. 1-8 and 21-34 in Hatcher. Hand in problems #2,3,4,5,7 of p. 38 in class on 9/22.

-Week 2: Hand in these problems in class on 9/8. Burgess' paper on the classification of surfaces can be found here.

-Week 0: Read Hatcher's notes on Introductory Point-set Topology, available here.


Lectures:  Tuesdays and Thursdays 3-4:15 pm in WXLR A113.

Material:  The main reference will be Algebraic Topology by Allen Hatcher (chapters 0, 1 and Appendix), available here. We will be covering the following topics: cell complexes, topological manifolds, Euler characteristic, classification of surfaces, fundamental groups, covering spaces and possibly some homology (time permitting).

Homework:  Assignments will be given online every other week, usually by Thursday, and will be due in class the following Thursday.

Exams:  There will be a Midterm and a Final exam. The Midterm exam will take place during class time on Thursday 10/13. The Final exam will take place on Tuesday 12/6, 2:30-4:20pm in WXLR A113 (standard University calendar).


Grading:  Homework will count for half of the final grade; the Midterm will count for 20% and the Final for 30% of the final grade.

Office hours:  Tuesdays 4:20-5:20 pm in my office, WXLR 431. If you would like to meet at another time, write me an email at paupert@asu.edu, or call me at 480-727-6661 to schedule an appointment.

Disability accommodation:  Qualified students with disabilities who will require disability accommodations in this class are encouraged to make their requests to me at the beginning of the semester either during office hours or by appointment. Note: Prior to receiving disability accommodations, verification of eligibility from the Disability Resource Center (DRC) is required. Disability information is confidential.

Academic integrity: "Academic honesty is expected of all students in all examinations, papers, laboratory work, academic transactions and records. The possible sanctions include, but are not limited to, appropriate grade penalties, course failure (indicated on the transcript as a grade of E), course failure due to academic dishonesty (indicated on the transcript as a grade of XE), loss of registration privileges, disqualification and dismissal. For more information, see http://provost.asu.edu/academicintegrity."