In this talk I will give some purely topological construction for hyperbolic 3-manifolds with infinitely generated fundamental group, this will let us construct many infinite-type hyperbolic 3-manifolds. Then, we will look at the set of hyperbolic structures that they can admit.
Links:
[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/de/node/3444
[3] https://www.mpim-bonn.mpg.de/de/node/3050