Termin: Detail

Wolfgang Lueck (Bonn)- Survey on aspherical manifolds

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We give a survey over aspherical closed manifolds. Aspherical is the purely homotopy theoretic condition that the universal covering is contractible. There are many well-known examples such as closed Riemannian manifolds with non-positive sectional curvature, but also very exotic examples such as closed aspherical manifolds that  do not admit a triangulation. We discuss some prominent conjectures, e.g., the Borel Conjecture about the topological rigidity, and the Singer Conjecture about the concentration of L^2-Betti numbers in the middle dimension.  The main point is to get a better understanding why the condition aspherical has so many consequences about the topology, geometry, algebra, and analysis about such manifolds.

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Beginn: 24. April 2024 16:00

Ende: 24. April 2024 17:00