Algebraic Topology: Mat 560
Math 560
TTh Fine 1201, 11am-12:20pm
Instructor: Peter Ozsváth
phone: 609-258-4222
email:
petero@math.princeton.edu
office: 1106
Office Hours: Fridays at 10AM, starting Feb 6
Grader: Gheehyn Nahm
UCA: Kashti Umare
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:
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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:
There will be no class on Thursday, April 2nd.
Grading:
The course grade is calculated as follows:
-
Final: 45%
-
Midterm: 30%
-
Homework: 25%
Attendance:
Although you are not graded for attendance, I expect you to come to class.
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.
It is OK to work with other people in the class. But if you do so, please state exactly what help you got.
It is possible to find solutions to many Hatcher problems by googling. Do not do this.
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 Thursday, Feb 12th at 11:59PM.
Chapter 0. p 19: 6, 10, 17
Chapter 1.1 pp 38-39: 3, 17
Chapter 1.2 pp 52-55: 7, 8, 22
Midterm Exam:
There will be an in-class Midterm exam.
Final Exam:
There will be an in-class final exam.