Prof. Wolfgang Lück:
Aspherical manifolds, what we know and what we do not know
Time and place
Thursday, 24.11.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
Abstract
Aspherical closed manifolds arise very often in topology, for\ninstance in low dimensional topology,\nclosed Riemannian manifolds with non-positive sectional curvature and so on. We\nwant to give a survey about open problems (and their status) such as the\nBorel Conjecture about topological rigidity, the Novikov Conjecture about the\ntopological invariance of higher signatures,\nthe Singer Conjecture about the distribution of L^2-Betti numbers,\napproximation of L^2-torsion,\nand the realizablility of Poincare duality groups as fundamental groups of\naspherical closed manifolds. Moreover, we present results about the rational\nhomotopy groups of\nthe group of diffeomorphisms and homeomorphisms of aspherical closed manifolds\nand the problem which hyperbolic groups have the standard sphere as boundary.\n\n\n\n\n\n\n