Algebraic Topology

Instructor: Peter Ozsváth
phone: 609-258-4222
email: petero@math.princeton.edu
Office: 1106
Office Hours: 11-12 on Fridays; or by appointment. Room 1106.

Grader: Gheehyun Nahm
Office Hours: 1:30-2:30 on Fridays, Common Room
UCA: Elie Belkin
Office Hours: TBA
UCA: Kaivalya Kulkarni
Office Hours: TBA

The course:

This is an introduction to algebraic topology. In the past, I mostly followed Allen Hatcher's Algebraic Topology. (Primarily Chapters 1-3.) This book is available online, as well. I may veer a little bit from my usual material time around, though. We will start with fundamental group and covering spaces, and then go on to singular homology and cohomology. We might make a little digression into differential topology at some point. Some background (for example, some group theory and point set topology) will be filled in as needed. Additional reading:

Munkres Topology, for review of point set topology.
J. Milnor Topology from a differentiable point of view, for a rapid and very elegant introduction to differential topology.
R. Bott and L. P. Tu Differential forms in Algebraic Topology for further reading in topology.
Greenberg and Harper Algebraic Topology. A classic.
E. Spanier Algebraic Topology. Another classic.

Announcements:

Announcements posted here.

Grading:

The course grade is calculated as follows:

Final: 45%
Midterm: 30%
Homework: 25%

Homework:

Homework constitutes a fairly small fraction of the grade. However, it will be impossible to do well on the exams without the working knowledge acquired by doing homework. Homework will be given once a week or two. Late work will not be accepted, except under special circumstances. In case of such circumstances, please make arrangements in advance with the grader.

Assignments:

Homework 1. Due Tues, Feb 11th
Chapter 0. p 19: 6, 10
Chapter 1.1 pp 38-39: 3, 17
Chapter 1.2 pp 52-55: 7, 8, 22

Homework 2 due Tues, Feb 25th at 11 AM.
Chapter 1.3 pp 79-81:2, 4, 6, 9, 10, 12, 26

Homework 3 due Tues, Mar 18
Chapter 2.1 p 131: 11, 12, 15, 20, 22
Chapter 2.2 pp 155-158: 2, 4, 5, 8, 9, 12.

Midterm Exam:

There will be an in-class midterm, on Thursday, March 20th, during class time. The exam will be a closed-notes exam, and it will cover fundamental groups, covering spaces, and some homology.

Final Exam:

There will be a take-home final.