Generating functions on epimorphisms between 2-bridge knot groups

Abstract

We have the generating function which determines the number of [Formula: see text]-bridge knot groups admitting epimorphisms onto the knot group of a given [Formula: see text]-bridge knot, in terms of crossing number. In this paper, we will refine this formula by taking into account genus as well as crossing number. Next, we determine the number of epimorphisms between fibered [Formula: see text]-bridge knot groups. Moreover, we discuss degree one maps and [Formula: see text]-bridge knots with unknotting number one.