of the Manifold Atlas ( 2012 ) 1 – 17 Aspherical manifolds *
نویسنده
چکیده
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, has many striking implications about the geometry and analysis of the manifold or its universal covering, and about the ring theoretic properties and the Kand L-theory of the group ring associated to its fundamental group. 57N99, 19A99, 19B99, 19D99, 19G24, 20C07, 20F25, 57P10
منابع مشابه
Aspherical Manifolds, Relative Hyperbolicity, Simplicial Volume, and Assembly Maps
This paper contains examples of closed aspherical manifolds obtained as a by-product of recent work by the author [Bel] on the relative strict hyperbolization of polyhedra. The following is proved. (I) Any closed aspherical triangulated n-manifold M with hyperbolic fundamental group is a retract of a closed aspherical triangulated (n+ 1)manifold N with hyperbolic fundamental group. (II) If B1, ...
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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, has many striking implications about the geometry and analysis of the manifold or ...
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