Seminar

Mixed-platonic 3-manifolds: at the interface of algebra, combinatorics, and (hyperbolic) geometry

I'll introduce a class of cusped hyperbolic 3-manifolds that we call mixed-platonic, composed of regular ideal hyperbolic polyhedra of more than one type. For reasons I'll give in the talk, we are interested in such manifolds that are complements of knots in the three-sphere. One such "knot complement" has been known for some time to fit this description; whether there are any more is an open question.