Seminar

This seminar series will take place on UC Berkeley campus, in Evans Hall room 939.

The figure eight knot (and its complement) is a pervasive example in 3-manifold topology and knot theory. It is the first hyperbolic knot to be discovered, and possesses many unique properties: it is arithmetic, smallest volume, most number of exceptional fillings, fibered with fixed-point free monodromy, its 3-fold cyclic cover is Euclidean, among several other facts. It has also featured in many papers as a first example of a class of phenomena, such as: a link of a real algebraic singularity; admits a spherical CR structure; a universal knot; fundaemental group is biorderable, profinitely rigid, and conjugacy separable; classification of unknotting changes; detected by knot Floer homology and Khovanov homology. This talk will serve as an introduction to these and more properties of the figure eight knot. Subsequent talks then will focus on specific properties.