Topological Methods in Combinatorics and Geometry
Topological Methods in Combinatorics and Geometry
Pre-Doc Course, Oct 25- Nov 23
Lecture: Thursdays and Fridays 9:15-12:00
Room: IFW B42
Office: IFW B45.1
email: matousek in domain kam.mff.cuni.cz
Assistant:
Tibor Szabó
Office: IFW B48.1
email:
szabo@inf.ethz.ch
tel: 01/632-0858
Course description
One of the important tools for proving results in discrete mathematics are
theorems from algebraic topology, most notably various fixed-point theorems.
The course covers the basic topological notions and results (simplicial
complexes, Borsuk-Ulam theorem and its generalizations etc.) and proofs of
several combinatorial and geometric results. The topological notions and
results are kept on very elementary level. In particular, knowledge of
elementary algebraic topology, like introductory homology theory, is
(encouraged but) not required.
Lecture notes
Here are the
full lecture notes (including index and
exercises) in A4 format. It should be the most recent version,
with known mistakes fixed.
Further suggested reading
For general background in topology, we recommend reading
in the following books:
- J. R. Munkres: Topology (A first course), Prentice Hall, 2000 (this is the 2nd ed., the older one is also good); this is an introduction to general topology
and a just a little of algebraic topology
-
J. R. Munkres: Elements of algebraic topology, Addison-Wesley, Reading, MA, 1984
-
A. Hatcher: Algebraic Topology, Cambridge University Press, 2001.
Scheduled to appear only in November, BUT here is an
electronic version
for download
Algebraic topology is generally useful and it probably pays off to
study these books carefully. For the purposes of the course, though,
it may be helpful even to read the beginning of one of these books once
or twice, skimming over the details,
in order to get used to the basic topological notions.
In particular, do not miss Chapter 0 in Hatcher's book, where
many things are beautifully explained on an intuitive level!
The next step in that book would be Chapter 2 (homology).
We won't make much use of the fundamental group, which is the subject
of Chapter 1.
