Abstract: A Bianchi group is $PSL(2,O_d)$ for some $O_d$, the ring of integers in a quadratic imaginary field. These are some of the first and most well-studied Kleinian groups. A fully augmented link (FAL) is a natural diagrammatic object and its complement tends to have nice geometric properties as well. Some of the simplest FAL complements also cover the quotients of $H^3$ by Bianchi groups. In some sense, both objects give standard examples in 3-manifold topology.
Two natural questions are then: 1) which fully augmented link complements have this property? 2) which Bianchi groups contain a fully augmented link group? As part of joint work (in progress) with Will Worden, we can answer both of these questions save a few boundary cases. An interesting corollary of our work so far is that no FAL complement decomposes into regular ideal tetrahedra.
To add/edit talks, please log in on the department web page, then return to Announce. Alternatively if you know the Announce
username/password, click the link below: