Coherence of Limit Points in the Fibers over the Asymptotic Teichmueller Space

摘要

We consider the infinite dimensional Teichmueller space of a Riemann surface of general type. On the basis of the fact that the action of the quasiconformal mapping class group on the Teichmueller space is not discontinuous, in general, we divide the Teichmueller space into two disjoint subsets, the limit set and the region of discontinuity, according to the discreteness of the orbit by a subgroup of the quasiconformal mapping class group. The asymptotic Teichmueller space is a certain quotient space of the Teichmueller space and there is a natural projection from the Teichmueller space to the asymptotic Teichmueller space. We consider the fibers of the projection over any point in the asymptotic Teichmueller space, and show a coherence of the discreteness on each fiber in the Teichmueller space.