Connectivity in the space of framed hyperbolic 3-manifolds
Connectivity in the space of framed hyperbolic 3-manifolds
We prove that the space $\mathcal{H}_\infty$ of framed infinite volume hyperbolic $3$-manifolds is connected but not path connected. Two proofs of connectivity of this space, which is equipped with the geometric topology, are given, each utilizing the density theorem for Kleinian groups. In particular, we decompose $\mathcal{H}_\infty$ into a union …