Title: Knots and their (embedded) graphs
| Speaker: | Iain Moffatt |
| Affiliation: | Royal Holloway University of London |
| Room: | MC 5479 |
Abstract:
There is a classical and well-known way to describe an alternating knot or link as a plane graph, known as its Tait graph. In fact, this sets up a 1-1 correspondence between plane graphs and alternating link diagrams. Alternating knots and links, however, form a very special class. What about non-alternating ones?
In this talk I'll describe a recent extension of Tait graphs that gives a way to describe any knot or link diagram, not just an alternating one, as a graph in a surface. While every plane graph arises as the Tait graph of a unique link diagram, not every embedded graph represents a link diagram. Furthermore, although a Tait graph describes a unique link diagram, the same embedded graph can represent many different link diagrams. One is then led to ask which embedded graphs represent link diagrams, and how link diagrams that have the same embedded graphs are related to one another. In this talk I'll offer answers to these questions.