Olivetti Club

Colby KellnCornell University
The Figure 8 Knot and Volumes

Tuesday, November 8, 2022 - 5:40pm
Malott 406

The figure 8 knot is likely the first knot you would learn to tie for top-rope rock climbing. I will introduce you to the figure 8 knot in a different context: that of low dimensional topology and hyperbolic geometry. We will explore Thurston's very visual proof that the figure 8 knot compliment is a hyperbolic 3-manifold. Next, since the volume of a hyperbolic $n$-manifold for $n\geq 3$ is a topological invariant, we will spend some time on volumes of hyperbolic manifolds, ending with a short survey of the state of the art knowledge of the minimum volume hyperbolic manifolds.