Let $M$ be a hyperbolic $n$-manifold whose cusps have torus
cross-sections. We constructed a variety of nonpositively and negatively
curved spaces as "$2\pi$-fillings" of $M$ by replacing the cusps of $M$
with compact "partial cones" of their boundaries. We show that the
simplicial volume of any such $2\pi$-filling is positive, and bounded
above by Vol$(M)/v_n$, where $v_n$ 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. This is
a joint work with J. Manning.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/249