Punctured Torus Groups and 2-Bridge Knot Groups (I)

This monograph is Part 1 of a book project intended to give a full account of Jorgensen's theory of punctured torus Kleinian groups and its generalization, with application to knot theoryIn this monograph, we give an elementary and self-contained description of Jorgensen's theory with a complete proof. Through various informative illustrations, readers are naturally led to an intuitive, synthetic grasp of the theory, which clarifies how a very simple fuchsian group evolves into complicated Kleinian groups.