Orbits and their accumulation points of cyclic subgroups of modular groups
The author discusses the geometry of elements of the Teichmüller group for Riemann surfaces of signature \((g,p)\). These can be classified as elliptic, parabolic, hyperbolic and pseudo-hyperbolic. She gives an elegant proof of an assertion of Bers that an invariant line of a hyperbolic element is unique. She also gives a new proof of an unpublished theorem of McCarthy which asserts that if \(\gamma_ 1\) is hyperbolic and if \(\gamma_ 2\) normalizes the cyclic group generated by \(\gamma_ 1\) then \(\gamma_ 2\gamma_ 1\gamma_ 2^{-1}=\gamma_ 1^{\pm1}\) and describes the possible \(\gamma_ 2\) more precisely. Finally she gives some further applications of the same techniques.
scientific article; zbMATH DE number 20410
scientific article