Geography & Evolution for Lens Space Surgeries
Dehn surgery ---removing a solid torus and regluing it in a possibly different way--- transforms one 3-manifold to another. One of the major open questions in the field is the Berge Conjecture, which posits a classification of the knots in \(S^3\) which yield lens spaces under surgery. In this talk, I'll describe a technique for building manifolds that admit lens space surgeries; among other properties, this construction provides a unified topological explanation for some sporadic examples found previously using a computer search. This is joint work with Ken Baker and Neil Hoffman.
Dr Joan Licata, Australian National University