_{posted 8 March 2007}

**Speaker:**Oliver Baues (TU Karlsruhe)

**Title:**"Constructions of aspherical manifolds"

**Date:**13th March 2007

**Abstract**

Given an abstract group $\Gamma$, there is the basic question if it is possible to construct compact aspherical smooth manifolds with fundamental group $\Gamma$, and also to understand the geometric properties of such manifolds. Ideally, one would like to classify them up to homeomorphism or up to diffeomorphism.

For example, 'most' polycyclic groups $\Gamma$ appear as fundamental groups of so called solvmanifolds. Another type of examples which appear in geometry are the fundamental groups of locally symmetric spaces. We would like to discuss a method which allows to build 'mixed' examples from these basic building blocks. This construction corresponds to the notion of group extension on the level of the fundamental group, and it has many interesting geometric properties.