Geodesic intersections and isoxial Fuchsian groups (Q2292299)

Two Fuchsian groups are isoaxial if they share the same set of axes. For instance, two commensurable groups (that is, if they share a common subgroup of finite index) are isoaxial. For a given Fuchsian group, its set of axes of hyperbolic elements depends on the commensurability class of the group. A natural question is whether isoaxiality implies commensurability. In the paper under review, the author shows that this holds for almost all Fuchsian groups. More precisely, he proves the following: For almost every point in the Teichmüller space of a hyperbolic surface, the corresponding Fuchsian representation of the fundamental group is deteremined by its axes. The paper contains also a discussion about angle spectra of Fuchsian groups and isoaxial groups having the same angles.