Exploring the quasi-fuchsian space for twice punctured torus
Abstract: In this talk I would like to provide a framework for studying twice punctured torus groups, and give a demonstration of an experimental computer program based on it. The framework is a direct extension of the concept of complex probability. Thus we can apply techniques developed for the study of once punctured torus groups to that of twice punctured torus groups in a natural fashon. While once punctured torus groups have some rigid structures and behave somehow nicely, twice punctured torus groups are considered to behave much more wildly and expected to show phenomena occuring in general quasi-fuchsian groups. Although the framework introduced here does not extends to more complex groups than twice punctured torus groups, we expect to get ideas about general quasi-fuchsian groups by studying twice punctured torus groups in this framework.