Planar Baumslag-Solitar actions

Following previous work, where representations of $BS(1,n)$ by planar orientation preserving homeomorphisms with linear diagonalizable conjugating element was studied, we consider the elliptic and parabolic cases. As an application, we prove that there are no faithful representations of $BS(1,n)$ by toral homeomorphisms with conjugating element the Dehn twist map.