The Goeritz groups of (1,1)-decompositions

A [Formula: see text]-decomposition of a link [Formula: see text] in a closed orientable [Formula: see text]-manifold [Formula: see text] is a decomposition of [Formula: see text] by a closed orientable surface of genus [Formula: see text] into two handebodies each intersecting the link [Formula: see text] in [Formula: see text] trivial arcs. The Goeritz group of that decomposition is then defined to be the group of isotopy classes of orientation-preserving homeomorphisms of the pair [Formula: see text] that preserve the decomposition. We compute the Goeritz groups of all [Formula: see text]-decompositions.