Algebraic Topology
Instructor: Peter Ozsváth
phone: 609-258-4222
email:
petero@math.princeton.edu
office: 1106
office hrs: 9-10AM Fridays; or by appointment.
Grader: Amitesh Datta
email:
amiteshd@math.princeton.edu
Office Hours: TBA
The course:
This is an introduction to algebraic topology, mostly
following Allen Hatcher's Algebraic Topology. (Primarily Chapters 1-3.)
This book is available online, as well.
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:
I have posted the exam outside my door. It is due on May 16th at 1PM.
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 Mon, Feb 15th at 11AM.
Chapter 0. p 19: 6, 10, 17
Chapter 1.1 pp 38-39: 3, 17
Chapter 1.2 pp 52-55: 7, 8, 22
Homework 2 due Mon, Feb 29th at 11AM.
Chapter 1.3 pp 79-:2, 4, 6, 9, 10, 12, 26
Chapter 2.1 p 131: 11, 12, 15.
Homework 3 due Mon, Apr 4.
Chapter 2.2 p 155: 1, 4, 5, 9, 8, 12, 14
Chapter 2.2 p 157: 19, 20, 21, 22, 23.
Homework 4 due Mon, Apr 25.
Chapter 3.1 p 204: 3, 5, 8, 9
Chapter 3.2 p 228. 2, 3, 6, 7, 11, 15
Midterm Exam:
There was a mid-term exam on March 7th.
Final Exam:
The take-home Final is printed out and it is in the mailbox outside my office. It is due at 1:00 PM on Monday, May 16th.