On homology 3-spheres defined by two knots

Masatsuna Tsuchiya

Published 2014-01-29, updated 2014-10-28Version 2

We show that if each of $K_1$ and $K_2$ is a trefoil knot or figure eight knot, the homology 3-sphere defined by the Kirby diagram which is a simple link of $K_1$ and $K_2$ with framing (0, n) is represented by an n-twisted Whitehead double of $K_2$ .