The goal of this talk is to construct new examples of hyperbolic
aspherical complexes. More precisely, given an aspherical simplicial
complex P and a subcomplex Q of P, we are looking for conditions under
which the complex obtained by attaching a cone of base Q on P remains
aspherical. If Q is a set of loops of a 2-dimensional complex, J.H.C.
Whitehead proved that this new complex is aspherical if and only if the
elements of the fundamental group of P represented by Q do not satisfy
any identity. To deal with higher dimensional subcomplexes we use small
cancellation theory and extend the geometric point of view developed by
T. Delzant and M. Gromov to rotation families of groups. In particular
we obtain hyperbolic aspherical complexes obtained by attaching a cone
over the "real part" of a hyperbolic complex manifold.