Abstract

Johannson’s characteristic submanifold theory provides an effective and convenient way to decompose a three-manifold, and has been used extensively in studying automorphisms of a three- manifold. In this talk, I will explain how the theory can be applied to classifying handlebody-knots, which are embedded handlebodies in the 3-sphere, and computing their symmetry groups. The talk will begin with a quick review of characteristic submanifold theory, which is followed by a short introduction to the Koda-Ozawa classification of essential annuli in handlebody-knot exteriors. Based on them, the notion of a characteristic diagram of a handlebody-knot will be introduced, and a classification result on irreducible, atoroidal handlebody-knots, via characteristic diagrams, will be presented. I will wrap up the talk with some applications to handlebody-knot symmetry.

WebEx Link

https://nationaltaiwanuniversity-ksz.my.webex.com/nationaltaiwanuniversity-ksz.my/j.php?MTID=ma8c884823cca3368afa5972a82b3f93e