Topology Seminar: Dale Rolfson

For any non-negative integer n there exist n-cusped hyperbolic 3-manifolds of minimal possible volume.  They are sometimes not unique.  For example there are exactly two distinct minimal 1-cusped examples: the figure eight complement, and another which is not a knot complement.  Similarly there are distinct 2-cusped examples.  I will show how these examples differ in terms of properties of their fundamental groups.  In particular, in the pairs of examples in the 1 or 2 cusped case, one has bi-orderable fundamental group while the other’s group is not orderable.  This is a preliminary announcement of work in progress with Eiko Kin (Osaka).