Hyperbolic Knot Complements without Closed Embedded Totally Geodesic Surfaces
نویسندگان
چکیده
It is conjectured that a hyperbolic knot complement does not contain a closed embedded totally geodesic surface. In this paper, we show that there are no such surfaces in the complements of hyperbolic 3-bridge knots and double torus knots. Some topological criteria for a closed essential surface failing to be totally geodesic are given. Roughly speaking, sufficiently ‘complicated’ surfaces can not be totally geodesic. 1991 Mathematics subject classification (Amer. Math. Soc.): 57M25,57M50.
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