Geodesic surfaces in the complement of knots with small crossing number

arXiv2207.14792MaRDI QIDQ6406488

Khanh Le, Rebekah Palmer

Publication date: 29 July 2022

Abstract: In this article, we investigate the problem of counting totally geodesic surfaces in the complement of hyperbolic knots with at most 9 crossings. Adapting previous counting techniques of boundary slope and intersection, we establish uniqueness of a totally geodesic surface for the knots $7_4$ and $9_{35}$. Extending an obstruction to the existence of totally geodesic surfaces due to Calegari, we show that there is no totally geodesic surface in the complement of 47 knots.

Mathematics Subject Classification ID

Knot theory (57K10) Hyperbolic 3-manifolds (57K32)

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