Visualization of hyperbolic surfaces via generic fundamental polygons, and its applications on the theory of the canonical decomposition

为了利用计算机实现双曲曲面的可视化，本研究需要对双曲曲面进行适当的符号处理。我得到了一个这样的象征性实现的原型，不仅是双曲的，而且是一般的。这种实现的一个优点是可以检测曲面的双曲性。另一个结果是，我得到了当Fuchsian群的一般基本多边形的组合类型的中心在双曲平面无穷远的圆上时其稳定性的一个证明。这一结果对应于一般基本多边形的相同性质的已知结果，其中心在双曲平面上。

To visualize hyperbolic surfaces by using of computer, it is required to decide suitable symbolical treatment of such surfaces in this research. I obtained a prototype of such symbolical realization of, not only hyperbolic but also general, surfaces. An advantage of this realization is to detect hyperbolicity of surfaces. Another result is this research is that I obtained a proof of stability of the combinatorial type of generic fundamental polygons of Fuchsian groups when their centers are on the circle at infinity of the hyperbolic plane. This result corresponds to a known result of the same property of generic fundamental polygons with their centers in the hyperbolic plane.