Networking Seifert surgeries on knots II: The Bergeʹs lens surgeries

In [A. Deruelle, K. Miyazaki, K. Motegi, Networking Seifert surgeries on knots, Preprint], we have defined the Seifert Surgery Network consisting of all the integral Dehn surgeries on knots in S 3 yielding Seifert fiber spaces, where Seifert fiber spaces may have fibers of indices zero as a degenerate case. In this paper we focus on lens surgeries, i.e. Dehn surgeries on knots which yield lens spaces. J. Berge [J. Berge, Some knots with surgeries yielding lens spaces, unpublished manuscript] gave a list of twelve infinite families of lens surgeries, which is conjectured to be a complete list of lens surgeries. We locate the Bergeʹs lens surgeries in the Seifert Surgery Network, and show that in the network, they are “close” to Seifert surgeries on torus knots.