MATH 468
Topology
Fall, 2002
TIME: MWF 12:50-01:40 PM. ROOM: 229 HAYE
INSTRUCTOR: Laurence Taylor
OFFICE: 246 HAYE PHONE: 1-7468
EMAIL: taylor.2@nd.edu
OFFICE HOURS: 3-4 Monday and Tuesday and by appointment
TEXT:
When Topology Meets Chemistry by
Erica Flapan
Additional material will be supplied by the instructor.
- Here is an installment.
- Here is installment two (updated).
- Here is installment three, which gives
an unlink algorithm.
- Here is installment four.
- Here is installment five (plus answers to the homework).
- Here is the last installment.
- Here is a set of solutions for the final.
FINAL: Wednesday, December 18, 2002 4:15-6:15pm in the regular classroom.
- Assignment 1 due Friday, Sept. 6, in class is here.
- Assignment 2 due Friday, Sept. 20, in class is here.
- Assignment 3 due Monday, Sept. 30, in class is the exercise at the end
of the first installment of additional material.
- Assignment 4 due Friday, Oct. 18, in class. There are three exercises
in the second installment of additional material.
Here is a calculation of the HOMFLY polynomials of some of the knots and
links that occur in this material.
- Assignment 5 due Monday, Nov. 11, in class. It is the assignment at the end
of installment four.
- A copy of assignment 6, due Monday, Nov. 25, in class, is here.
- A copy of assignment 7, due Monday, Dec. 9, in class, is at the end of here.
- A copy of the final, due Wednesday, Dec. 18, at 4:15pm is here.
This is a course in topological chemistry,
in particular the subject of stereoisomers.
These are long molecules which can be considered
as graphs and how the graph is embedded in
three-space profoundly affects the chemical
behavior of the compound.
Examples range from limonene, which smells either like
lemon or like orange depending on the embedding, to
Thalidomide, which is a cure for morning sickness in one
embedding but causes severe birth defects in another.
There also are interesting problems involving DNA.
Since this is a mathematics course we will abstract chemistry
questions to questions about the embeddings of graphs
into three-space and develop techniques for distinguishing
such embeddings.
The book concentrates on distinguishing chiral embeddings
from non-chiral ones, a central problem in
knot theory and its generalizations to graphs.
This is an active area
of current mathematical research.
Some web links
Topology and DNA.
The Knot Plot Site
Chiral Information Home Page
Chiral Molecules, Structures and Materials
See definition 4
The Chirality of a Knot
Knots on the Web
And so forth and so on.
