Torus knots and links in V1 that are invariant under the ℤm × ℤl-actions on V1 that form the quotient orbifold (A0,k)

Abstract

We demonstrate how the genus one handlebody orbifold [Formula: see text] is obtained as a quotient of orientation preserving [Formula: see text]-action on the solid torus [Formula: see text], where [Formula: see text], [Formula: see text], and [Formula: see text] are positive integers, [Formula: see text] divides [Formula: see text] and [Formula: see text] divides [Formula: see text]. We determine the torus knots and links in [Formula: see text] that are invariant under the corresponding action. In that case, the image of [Formula: see text] in [Formula: see text] is always a torus knot or link on the boundary of [Formula: see text]. We compute the image of [Formula: see text] in [Formula: see text] in both cases [Formula: see text] and [Formula: see text]. Finally, we lift the torus knots and links in [Formula: see text] to [Formula: see text] and compute their images in [Formula: see text].