Georgia Institute of Technology College of Sciences

The figure 8 knot is the simplest hyperbolic knot. In the late 1970s, Thurston studied how to construct hyperbolic manifolds from ideal tetrahedra. In this talk, I present the Thurston’s theory and apply this to the figure 8 knot. It turns out that every Dehn surgery on the figure 8 knot results in a hyperbolic manifold except for 10 exceptional surgery coefficients. If time permits, I will also introduce the classification of tight contact structures on these manifolds. This is a joint work with James Conway.