Algebraic Topology I, 18.905
Instructor: Peter Ozsváth
phone:
email:
petero@math.mit.edu
office: 2-341
office hrs: Fridays 3-4pm; or by appointment.
Grader: Ailsa Keating
email:
ailsa@math.mit.edu
Office Hours: Tuesdays 5-6pm
The course:
This is an introduction to algebraic topology. I
will basically follow Allen Hatcher's Algebraic Topology. (Mainly chapters 2 and 3, but some of 0 and 1 as well.)
This book is available online, as well.
The course will start with a quick review of
fundamental group and covering spaces. We will then
cover singular homology and cohomology.
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:
The grader will have office hours (listed above).
Homework is now due in her office (see below).
The midterm is coming up (also see below).
There will be two office hours on Wed, Dec 15th: 12-1pm and 3-4pm.
Grading:
The course grade is calculated as follows:
-
Final: 50%
-
Midterm: 30%
-
Homework: 20%
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 due by 3pm in Ailsa Keating's office, under the door
(2-586).
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 Wed, Sept 22nd at 12:05pm.
Chapter 0. p 19: 6, 10, 16, 17
Chapter 1.1 pp 38-39: 3, 17
Chapter 1.2 pp 52-55: 7, 8, 22
Chapter 1.3 pp 79-:2, 4, 6, 9, 10, 12, 26
Homework 2 due Wed, Oct 6 at 12:05pm.
Chapter 2.1 p 131: 11, 12, 15, 20, 22, 29
Chapter 2.2 p 155: 1, 4, 5, 9, 8, 12, 14
Homework 2 due Wed, Oct 20 at 12:05pm.
Chapter 2.2 p 157: 19, 20, 21, 22, 23, 34.
Homework 3 due Wed, Oct 6 at 12:05pm.
Chapter 2.1 p 131: 11, 12, 15, 20, 22, 29
Chapter 2.2 p 155: 1, 4, 5, 9, 8, 12, 14
Homework 4 due Wed, Nov 17th.
Chapter 3.1 p 204: 3, 5, 8, 9, 12
Chapter 3.2 p 228. 1, 2, 3, 6, 7, 11, 15
Homework 5 due Fri, Dec 3rd.
Chapter 3.3 p 257: 2, 6, 7, 8, 9*, 10*, 11*, 17*.
*=optional problem.
Midterm Exam:
The midterm exam will be an in-class exam
on Oct 25th, at our usual class time.
Final Exam:
The final exam is a 3-hour exam on Friday, Dec 17th from 9am-12pm. It will be in Walker Room 50-340.