Let be a hyperbolic
–manifold
whose cusps have torus cross-sections. In an earlier paper, the authors
constructed a variety of nonpositively and negatively curved spaces as
“–fillings” of
by replacing
the cusps of
with compact “partial cones” of their boundaries. These
–fillings are closed
pseudomanifolds, and so have a fundamental class. We show that the simplicial volume of any such
–filling is positive, and
bounded above by , where
is the volume of a regular
ideal hyperbolic –simplex.
This result generalizes the fact that hyperbolic Dehn filling of a
–manifold
does not increase hyperbolic volume.
In particular, we obtain information about the simplicial volumes of some
–dimensional
homology spheres described by Ratcliffe and Tschantz, answering
a question of Belegradek and establishing the existence of
–dimensional
homology spheres with positive simplicial volume.
