Totally Geodesic Spanning Surfaces of Knots and Links in 3-Manifolds

Benjamin Shapiro

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arXiv · 2402.04410

Totally Geodesic Spanning Surfaces of Knots and Links in 3-Manifolds

Benjamin Shapiro

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Abstract

I construct infinite families of knots and links with totally geodesic spanning surfaces, which we call TGS knots and TGS links, in various 3-manifolds. These 3-manifolds include thickened orientable surfaces, the sphere cross the circle, lens spaces, and the solid torus. The totally geodesic spanning surfaces of knots embedded in thickened orientable surfaces are also examples of totally geodesic spanning surfaces of virtual knots.

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Benjamin Shapiro. 2024-02-06. Totally Geodesic Spanning Surfaces of Knots and Links in 3-Manifolds. https://arxiv.org/abs/2402.04410

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