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Let M be a hyperbolic n–manifold whose cusps have torus cross-sections. In an
earlier paper, the authors constructed a variety of nonpositively and negatively
curved spaces as “2π–fillings” of M by replacing the cusps of M with compact
“partial cones” of their boundaries. These 2π–fillings are closed pseudomanifolds, and
so have a fundamental class. We show that the simplicial volume of any
such 2π–filling is positive, and bounded above by  , where vn is the
volume of a regular ideal hyperbolic n–simplex. This result generalizes the fact
that hyperbolic Dehn filling of a 3–manifold does not increase hyperbolic
volume.
In particular, we obtain information about the simplicial volumes of some
4–dimensional homology spheres described by Ratcliffe and Tschantz, answering a
question of Belegradek and establishing the existence of 4–dimensional homology
spheres with positive simplicial volume.
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