Surgery descriptions and volumes of Berge knots I: Large volume Berge knots

Abstract

By obtaining surgery descriptions of knots which lie on the genus one fiber of the trefoil or figure eight knot, we show that these include hyperbolic knots with arbitrarily large volume. These knots admit lens space surgeries and form two families of Berge knots. By way of tangle descriptions we also obtain surgery descriptions for these knots on minimally twisted chain links.