The universal commensurability Busemann horofunction compactified Teichmüller space

Abstract

AbstractIn this paper, the direct limit of Busemann horofunction compactified Teichmülller spaces is introduced. It is shown that the action of the universal commensurability modular group on is isometric and for any point in the universal commensurability Teichmüller space , its orbit under this action is dense in . Furthermore, we construct the direct limit of Busemann horofunction compactified moduli spaces by the characteristic towers and show that the subgroup of acts on to produce as the quotient. Finally, we get a formula of the limit distance between two Jenkins–Strebel rays in the universal commensurability Teichmüller space.