Weitere Informationen zum ausgewählten Kolloquiumsvortrag:

Aspherical manifolds, what we know and what we do not know

Prof. Wolfgang Lück

Donnerstag, 2016-11-24 17:00Uhr

Aspherical closed manifolds arise very often in topology, for instance in low dimensional topology, closed Riemannian manifolds with non-positive sectional curvature and so on. We want to give a survey about open problems (and their status) such as the Borel Conjecture about topological rigidity, the Novikov Conjecture about the topological invariance of higher signatures, the Singer Conjecture about the distribution of L^2-Betti numbers, approximation of L^2-torsion, and the realizablility of Poincare duality groups as fundamental groups of aspherical closed manifolds. Moreover, we present results about the rational homotopy groups of the group of diffeomorphisms and homeomorphisms of aspherical closed manifolds and the problem which hyperbolic groups have the standard sphere as boundary.