Topology
Math 131 - Harvard University - Fall 2013
10-11:30 Tu Th, 507 Science Center
Required Texts
- Munkres, Topology, 2nd edition, Prentice-Hall 2000
- Stillwell, Classical Topology and Combinatorial Group Theory, Springer, 1993
- Fulton, Algebraic Topology, Springer, 1995
Prerequisites:
Intended for undergraduate math majors.
Acquaintance with metric spaces (Math 25, 55, 101 or 112)
and groups (Math 101 or 122).
Students need to have a good feel for quotient groups and homomorphism,
and know the construction of free groups, the description of a group
by generators and relations, and the classification of free abelian
groups. This material can be found in Artin's Algebra .
Topics.
This course will cover the basics of topological spaces,
fundamental groups and covering spaces.
Topics include the following:
-
General Topology
- Set theory
- Topological spaces
- Continuous functions
- Connectedness
- Compactness
- Complete metric spaces
- Baire category
-
Algebraic Topology
- Homotopy theory
- Fundamental group
- Covering spaces
- Groups and gluing
- Graphs
- Surfaces
Reading and Lectures.
Students are responsible for all topics covered in
the readings and lectures. Lectures may go beyond the
reading, and not every topic in the reading will be
covered in class.
Grades.
Grades will be based on weekly homework (30%), an in-class midterm (30%)
and a take-home final (40%).
The lowest homework grade will be dropped.
Homework.
Homework will be assigned every week.
Late homework will not be accepted.
Collaboration between students is encouraged, but you
must write your own solutions, understand them and
give credit to your collaborators.
Calendar.
| 3 Sep (Tu) | First class |
| 24 Oct (Th) | In-class midterm |
| 28 Nov (Th) | Thanksgiving |
| 3 Dec (Tu) | Last class |
| 4-12 Dec (W-F) | Take-home final during reading period |