Jaun Pablo Díaz-González

Instituto de Matemáticas, Unidad Cuernavaca,
Universidad Nacional Autónoma de México,
Av. Universidad s/n, Col. Lomas de Chamilpa,
Cuernavaca, Mor. 62210, MEXICO.

Title: The figure-eight knot complement

Abstract: In this talk we visualize the figure-eight knot complement in the 3-sphere, and some other things inside it. We will see some geometrical and topological things, for example, open and closed geodesics, horocycles, and some generators and relations of its fundamental group. Also, we will visualize the fibration over the circle of the figure-eight knot complement.

At each stage, we will look through four eyeglasses, and we will show that the different views are equivalent: the topological complement itself, a handle decomposition, a PL-structure, and a symmetric hyperbolic tessellation.