The space of Kleinian punctured torus groups is not locally connected (Q630632)

The paper presents the first example of a deformation space of Kleinian groups which is not locally connected: as noted in the title, this is the space of Kleinian punctured torus groups, that is of free Kleinian groups on two generators whose commutator is parabolic. The paper starts with some general and historical background information on the topology of deformation spaces of Kleinian groups (e.g. phenomena such as bumping and self-bumping of the components of the interior of a deformation space), comparing the situation also with that for rational maps of \(\widehat{\mathbb C}\) (e.g., the conjecture that the Mandelbrot set is locally connected).