Topology
Math 131  Harvard University  Fall 2013
1011:30 Tu Th, 507 Science Center
Required Texts
 Munkres,
Topology,
2nd edition, PrenticeHall 2000
Recommended
 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 inclass midterm (30%)
and a takehome 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)  Inclass midterm 
28 Nov (Th)  Thanksgiving 
3 Dec (Tu)  Last class 
412 Dec (WF)  Takehome final during reading period 
