Math 99r - 3:00 - 6:00 Mondays - room 530 SC
Harvard University - Fall 2003
How is a sphere different from a torus?
A square-knot from a granny knot?
In this tutorial we will discuss topology in dimensions one, two and three,
with an emphasis on problems and examples.
Algebra and topology.
(Math 122 and 131). Some complex analysis (Math 113) may be useful.
Curtis T McMullen
Topics. Possible topics include:
- L. C. Kinsey,
Topology of Surfaces, Springer-Verlag, 1993
- A. Hatcher,
- R. Lickorish,
An Introduction to Knot Theory, Springer-Verlag, 1997
- Hoste et al, The First 1,701,936 Knots
Grades will be based on homework, attendance, a midterm paper
and a final paper.
- 1-dimensional manifolds
- Graphs, groups and covering spaces
- Boundaries of groups
- 2-dimensional manifolds
- Group presentations
- Euler characteristic
- Simple closed curves
- Dehn twists
- 3-dimensional manifolds
- Reidemeister moves
- Fundamental group
- Linking number
- Seifert surfaces
- Polynomial invariants
- M, 15 Sep. First class
- M, 13 Oct. Columbus day
- Tu, 11 Nov. Veterans day
- Th-F, 27-28 Nov. Thanksgiving
- M, 15 Dec. Last class
- M-F, 5-16 Jan. Reading period
Course home page: