Geodesic surfaces in the complement of knots with small crossing number

In this article, we investigate the problem of counting totally ge-odesic surfaces in the complement of hyperbolic knots with at most 9 cross-ings. Adapting previous counting techniques of boundary slope and inter-section, we establish uniqueness of a totally geodesic surface for the knots 74 and 935. Extending an obstruction to the existence of totally geodesic sur-faces due to Calegari, we show that there is no totally geodesic surface in the complement of 47 knots.