Abstract:Abstract. We show that any parabolic generating pair of a genus-one hyperbolic 2-bridge knot group is equivalent to the upper or lower meridian pair. As an application, we obtain a complete classification of the epimorphisms from 2-bridge knot groups to genus-one hyperbolic 2-bridge knot groups.
Let K, K ′ be two-bridge knots of genus n, k respectively. We show the necessary and sufficient condition of n in terms of k that there exists an epimorphism from the knot group of K onto that of K ′ .
Let K, K ′ be two-bridge knots of genus n, k respectively. We show the necessary and sufficient condition of n in terms of k that there exists an epimorphism from the knot group of K onto that of K ′ .
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