Discrete Geometry Group
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G. M. Ziegler:
Monday 8-12; MA 841
BMS course, taught in English!
Tutorials/Exercises by Bernd Gonska:
Wednesday 14-16; MA 644
or
Friday 12-14; MA 648 (start oct.23)
Please hand in your homeworks in the tutorial you are visiting.
A small pdf with definitions of wedge and suspension can be downloaded.
Topology "for the working mathematician"
Topology is an important, classical mathematical discipline, which treats interesting objects (such as the Klein bottle, Bing's house, manifolds, lens spaces, knots, ....) and which has produced spectacular successes in 20th century mathematics. A full study of topology is hard (it is a huge field that encompasses many subtle tools and theories); our modest goal here is an introduction and overview "for the working mathematician". Hence this is a Basic Course - primarily for mathematicians who do not head towards writing a thesis in topology, but who want to understand topological concepts, methods, and results that might be needed or useful tools at some point. Thus in this course (a 4 hour course, with exercises) we will treat some fundamentals of (point set) topology as well as many important parts of algebraic topology: This is supposed to be precise and concrete enough to enable you to perform topological arguments, and to apply topological results and techniques. We will also include proof ideas and sketches, which explain why all of this "works" - but we will not do the more complicated or longer proofs in detail, which would be required study for anyone striving to be a serious research topologist.An older complete version of them (in German) is available on the page of a previous installment of this course.
While you are encouraged to work on the problems in groups, we expect each student to formulate and hand in the solutions for themselves.
| # | problems | issue date | hand in date | note |
|---|---|---|---|---|
| 1 | |
October 14 | October 21/23 | only extra points |
| 2 | |
October 21 | October 29/31 | 2. problem: B2 has to be open! |
| 3 | |
October 29 | November 4/6 | |
| 4 | |
November 4 | November 11/13 | |
| 5 | |
November 11 | November 18/21 | |
| 6 | |
November 19 | November 25/27 | |
| 7 | |
November 25 | Dezember 2/4 | |
| 8 | |
Dezember 2 | Dezember 9/11 | In problem 1 "A" has to be replaced by "C" |
| 9 | |
Dezember 2 | Dezember 16/18 | G is a free abelian group like Z, Q or R. Gi is then a product like Z^3. But there are no cyclic parts. |
| X | |
Dezember 18 | January 6/8 | 3. problem: Delta has to be the boundary of a 3-simplex. |
| 11 | |
January 7 | January 13/15 | 3. problem: I fixed some brackets, and replaced H(X..) by a H(Y..). |
| definition | |
- | - | Definition of suspension, wedge and disjoint union |
| 12 | |
January 13 | January 20/22 | |
| 13 | |
January 22 | January 27/29 | |
| 14 | |
January 29 | February 3/5 |