Abstract. Given integers b, c, g, and n, we construct a manifold M containing a c-component link L so that there is a bridge surface Σ for (M, L) of genus g that intersects L in 2b points and has distance at least n. More generally, given two possibly disconnected surfaces S and S ′ , each with some even number (possibly zero) of marked points, and integers b, c, g, and n, we construct a compact, orientable manifold M with boundary S ∪ S ′ such that M contains a c-component tangle T with a bridge surface Σ of genus g that separates ∂M into S and S ′ , |T ∩ Σ| = 2b and T intersects S and S ′ exactly in their marked points, and Σ has distance at least n.

ABSTRACT. In 2001, J. Hempel proved the existence of Heegaard splittings of arbitrarily high distance by using a high power of a pseudo-Anosov map as the gluing map between two handlebodies. We show that lower bounds on distance can also be obtained when using a high power of a suitably chosen Dehn twist. In certain cases, we can then determine the exact distance of the resulting splitting. These results can be seen as a natural extension of work by A. Casson and C. Gordon in 1987 regarding strongly irreducible Heegaard splittings.