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 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.
Prerequisites:
Algebra and topology.
(Math 122 and 131). Some complex analysis (Math 113) may be useful.
Instructor:
Curtis T McMullen
Required texts
- C. Adams, The Knot Book, Henry Holt, 19??
- D. Rolfen, Knots and Links, available from the American Math. Soc. (but maybe not until Oct. 29)
- J. Stillwell,
Classical Topology and Combinatorial Group Theory
Springer-Verlag, 1993
- Click here for some errata
Other references
- L. C. Kinsey,
Topology of Surfaces, Springer-Verlag, 1993
- A. Hatcher, Algebraic Topology
- R. Lickorish,
An Introduction to Knot Theory, Springer-Verlag, 1997
- Hoste et al, The First 1,701,936 Knots
Topics. Possible topics include:
- 1-dimensional manifolds
- Graphs, groups and covering spaces
- Amenability
- Boundaries of groups
- 2-dimensional manifolds
- Group presentations
- Euler characteristic
- Homology
- Simple closed curves
- Dehn twists
- 3-dimensional 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
- Th-F, 27-28 Nov. Thanksgiving
- M, 15 Dec. Last class
- M-F, 5-16 Jan. Reading period