Algebraic Topology I
Instructor: Peter Ozsváth
phone: (212) 854-4757
email:
petero@math.columbia.edu
office: 620 Mathematics
office hrs: Monday 10:30-11:30; or by appointment.
Round table leader: Thomas Peters
email:
tpeters@math.columbia.edu
Roundtable: Thursdays, Math 528 from 5-6.
The course:
This is an introduction to algebraic topology. I
will basically follow Allen Hatcher's Algebraic Topology.
This book is available online, as well.
Topics will include: fundamental group, covering spaces, homology,
cohomology, homotopy groups.
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.
-
Fomenko, Fuks, Gutenmacher Homotopic Topology
for further reading in topology.
-
Greenberg and Harper Algebraic Topology.
A classic.
-
E. Spanier Algebraic Topology.
Another classic.
Announcements:
I will not be able to make my usual office hours on Monday, Oct
26th. They will be on Wed, Oct 28th instead at 10:30. (Or, of course, by appointment.)
The Midterm will be on Nov 4th.
Grading:
The course grade is calculated as follows:
-
Final: 50%
-
Midterm: 30%
-
Homework: 20%
Homework:
Homework 1: Hatcher Chapter 1:
Section 1.1: 17, 18
Section 1.2: 3, 4, 6, 9, 14, 16. Due Friday, Sept 25th at 5pm.
Homework 2: Hatcher Chapter 1:
Section 1.3: 3, 4, 5, 6, 9, 12, 18, 24. Due Friday, Oct 2nd at 5pm.
Homework 3: Hatcher Chapter 2:
Section 2.1: 4, 7, 8, 11, 12, 13, 14, 20, 21, 23. Due Friday, Oct 16th at 5pm.
Homework 4: Hatcher Chapter 2:
Section 2.2: 2, 3, 8, 9, 10, 12, 14, 19, 21, 34, 36. Due Friday, Oct 30th at 5pm.
Homework 4: Hatcher Chapter 3:
Section 3.1: 3, 7, 8, 9, 12 (further problems will go in Homework 5)
Due Friday, Nov 20th at 5pm.
Homework 5: Hatcher Chapter 3:
Section 3.2: 1, 2, 3, 6, 7, 11
Due Friday, Dec 4th at 5pm.
Midterm Exam:
The midterm exam will be an in-class exam on
Nov 4th. It will cover fundamental group and homology.