Totally Geodesic Spanning Surfaces of Knots and Links in 3-Manifolds by Ben Shapiro ’23
Wed, May 10th, 2023
1:00 pm - 1:45 pm
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Totally Geodesic Spanning Surfaces of Knots and Links in 3-Manifolds by Ben Shapiro ’23, Mathematics Senior Thesis Defense, Wednesday, May 10, 1 – 1:45 pm, North Science Building 113, Wachenheim.
Abstract: Totally geodesic surfaces are very beautiful and clean surfaces in hyperbolic 3-space. A spanning surface of a knot or link is a surface whose boundary is the knot or link. We conjecture that there exist knots and links in every representation of 3-dimensional space, or 3-manifold, which possess totally geodesic spanning surfaces. However, few such examples are known in 3-manifolds other than the 3-sphere. We will look at a number of different 3-manifolds and construct infinite families of knots and links which each have totally geodesic spanning surfaces.