Smallish knots in small 3-manifolds

Marc Culler

Abstract: This talk will be a continuation of, or at least somewhat related to, the talk by Peter Shalen which proceeds it. It will have been explained why it would be interesting and useful to be able to construct smallish knots, i.e. knots with irreducible complement and no meridian boundary slopes, in an irreducible non-Haken 3-manifold. The talk will discuss the possibility that edges in suitable 0-efficient triangulations may be smallish knots. The main theorem will describe some interesting combinatorial restrictions which must be satisfied by a 0-efficient triangulation, relative to a given edge, whenever the edge forms a knot which is not smallish.

created Thu May 18 14:54:17 PDT 2000