Aspherical Manifolds with Relatively Hyperbolic Fundamental Groups
نویسنده
چکیده
We show that the aspherical manifolds produced via the relative strict hyperbolization of polyhedra enjoy many group-theoretic and topological properties of open finite volume negatively pinched manifolds, including relative hyperbolicity, nonvanishing of simplicial volume, co-Hopf property, finiteness of outer automorphism group, absence of splitting over elementary subgroups, acylindricity, and diffeomorphism finiteness for manifolds with uniformly bounded simplicial volume. In fact, some of these properties hold for any compact aspherical manifold with incompressible aspherical boundary components, provided the fundamental group is hyperbolic relative to fundamental groups of boundary components.
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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