English

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.

Keywords

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