Totally Geodesic Spanning Surfaces of Knots and Links in 3-Manifolds
Geometric Topology
2024-12-24 v2
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.
Cite
@article{arxiv.2402.04410,
title = {Totally Geodesic Spanning Surfaces of Knots and Links in 3-Manifolds},
author = {Benjamin Shapiro},
journal= {arXiv preprint arXiv:2402.04410},
year = {2024}
}
Comments
39 pages, 26 figures