Geometric Topology
Math 99r  3:00  6:00 Mondays  room 530 SC
Harvard University  Fall 2003
Description.
How is a sphere different from a torus?
A squareknot from a granny knot?
In this tutorial we will discuss topology in dimensions one, two and three,
with an emphasis on problems and examples.
Prerequisites:
Algebra and topology.
(Math 122 and 131). Some complex analysis (Math 113) may be useful.
Instructor:
Curtis T McMullen
Required texts
Other references
 L. C. Kinsey,
Topology of Surfaces, SpringerVerlag, 1993
 A. Hatcher,
Algebraic Topology
 R. Lickorish,
An Introduction to Knot Theory, SpringerVerlag, 1997
 Hoste et al, The First 1,701,936 Knots
Topics. Possible topics include:
 1dimensional manifolds
 Graphs, groups and covering spaces
 Amenability
 Boundaries of groups
 2dimensional manifolds
 Group presentations
 Euler characteristic
 Homology
 Simple closed curves
 Dehn twists
 3dimensional manifolds
 Knots
 Reidemeister moves
 Coloring
 Fundamental group
 Tangles
 Linking number
 Seifert surfaces
 Polynomial invariants
Grades.
Grades will be based on homework, attendance, a midterm paper
and a final paper.
Calendar.
 M, 15 Sep. First class
 M, 13 Oct. Columbus day
 Tu, 11 Nov. Veterans day
 ThF, 2728 Nov. Thanksgiving
 M, 15 Dec. Last class
 MF, 516 Jan. Reading period
