New development of the theory of infinite dimensional Teichmuller spaces: construction of moduli spaces

关于无限维Teichmuller空间中Teichmuller模变换的分类，我们研究了无限离散型变换和散度型变换的性质。我们还观察了作用在渐近Teichmuller空间上的渐近Teichmuller模变换，得到了一个有限阶的充分条件。此外，对于稳定的拟共形映射类群的一个子群，我们观察到作用在渐近共形类空间上的不连续性。

On the classification of the Teichmuller modular transformations in infinite dimensional Teichmuller spaces, we investigated properties of transformations of infinite discrete type and those of divergent type. We also observed asymptotic Teichmuller modular transformations acting on asymptotic Teichmuller spaces and obtained a sufficient condition to be of finite order. Furthermore, for a subgroup of the quasiconformal mapping class group that is stationary, we observed discontinuity of the action on the space of asymptotically conformal classes.