Consider n particles moving in space (e.g. n point-like masses of a mechanical system). The set of all possible positions of these points is called the configuration space of n ... Lesen Sie weiter
Consider n particles moving in space (e.g. n point-like masses of a mechanical system). The set of all possible positions of these points is called the configuration space of n points in X, if X is the space that the particles move in. These spaces have been intensely studied for a long time and are still being investigated because of their importance for many areas of mathematics and physics. For example last year Günter Ziegler and Pavle Blagojevic, both from the FU, solved a conjecture in discrete geometry with the help of a particularly nice model for the configuration spaces of Euclidean space and the use of cohomological methods. Configuration spaces also play an important role in homotopy theory and in the study of braid groups and mapping class groups of surfaces. With regard to the cohomolgy of these spaces there will be in January 2014 a joint block seminar by Gavril Farkas (HU) and Holger Reich (FU).
In this course we introduce basic concepts for understanding these spaces, explore their relationship to braids and mapping class groups and get some information about their cohomology groups. Part of the course can be seen as a preparation for the above mentioned block seminar. Schließen