Abstract
This is a survey on known results and open problems about closed aspherical manifolds, i.e., connected closed manifolds whose universal coverings are contractible. Many examples come from certain kinds of non-positive curvature conditions. The property aspherical, which is a purely homotopy theoretical condition, implies many striking results about the geometry and analysis of the manifold or its universal covering, and the ring theoretic properties and the K- and L-theory of the group ring associated to its fundamental group. The Borel Conjecture predicts that closed aspherical manifolds are topologically rigid. The article contains new results about product decompositions of closed aspherical manifolds and an announcement of a result joint with Arthur Bartels and Shmuel Weinberger about hyperbolic groups with spheres of dimension ≥ 6 as boundary. At the end we describe (winking) our universe of closed manifolds.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
