Distance to longitude

Abstract

Let [Formula: see text] be a hyperbolic knot in the [Formula: see text]-sphere. If a [Formula: see text]-Dehn surgery on [Formula: see text] produces manifold with an embedded Klein bottle or essential [Formula: see text]-torus, then we prove that [Formula: see text], where [Formula: see text] is the genus of [Formula: see text]. We obtain different upper bounds according to the production of a Klein bottle, a non-separating [Formula: see text]-torus, or an essential and separating [Formula: see text]-torus. The well known examples which are the figure eight knot and the pretzel knot [Formula: see text] reach the given upper bounds. We study this problem considering null-homologous hyperbolic knots in compact, orientable and closed [Formula: see text]-manifolds.