  Using results in a previous paper "Non-semistable exceptional objects in
hereditary categories", we focus here on studying the topology of the space of
Bridgeland stability conditions on $D^b(Rep_k(Q ))$, where $Q$ is the acyclic
triangular quiver (the underlying graph is the extended Dynkin diagram
$\widetilde{\mathbb A}_2$). In particular, we prove that this space is
contractible (in the previous paper it was shown that it is connected).
