Koji Fujiwara

title: CAT(0) and CAT(-1) fillings of hyperbolic manifolds

abstract:
This is a joint work with Jason Manning.
We give new examples of hyperbolic and relatively hyperbolic groups of
cohomological dimension $d$ for all $4 \le d$.
These examples result from applying CAT(0)/CAT(-1) filling constructions
(based on singular doubly warped products)
to finite volume hyperbolic manifolds with toral cusps. Our construction
is a generalization of Gromov-Thurston's 2$\pi$-theorem
to CAT spaces. It is also a geometric realization of a group theoretic
analogues of 2$\pi$-theorem due to Grove-Manning and Osin.
A special case of our construction has been obtained by Mosher-Sageev.