Geometriae Dedicata

, 129:119 | Cite as

Aspherical manifolds with relatively hyperbolic fundamental groups

  • Igor Belegradek
Original Paper


We show that the aspherical manifolds produced via the relative strict hyperboli- zation 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, and acylindricity. 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. We also show that no manifold obtained via the relative strict hyperbolization can be embedded into a compact Kähler manifold of the same dimension, except when the dimension is two.


Relatively hyperbolic Hyperbolization of polyhedra Aspherical manifold Splitting Simplicial volume Co-Hopfian Kähler 

Mathematics Subject Classification (2000)



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Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA

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