Genus two Goeritz groups of lens spaces

Given a genus-$g$ Heegaard splitting of a 3-manifold, the Goeritz group is defined to be the group of isotopy classes of orientation-preserving homeomorphisms of the manifold that preserve the splitting. In this work, we show that the Goeritz groups of genus-2 Heegaard splittings for lens spaces $L(p, 1)$ are finitely presented, and give explicit presentations of them.