Contents
Introduction xv
Chapter 1. The modular group and elliptic function theory 1
§1. Mobius transformations 2
§2. Riemann surfaces 4
§3. Kleinian groups 5
3.1. Generalities 5
3.2. The situation of interest 8
§4. The elliptic paradise 9
4.1. The family of tori 9
4.2. The algebraic curve associated to a torus 14
4.3. Invariants for tori 23
4.4. Tori with symmetries 28
4.5. Congruent numbers 31
4.6. The plumbing construction 31
4.7. Teiehmuller and moduli spaces for tori 33
4.8. Fiber spaces - the Teiehmuller curve 33
§5. Hyperbolic version of elliptic function theory 37
5.1. Fuchsian representation 38
5.2. Symmetries of once punctured tori 41
5.3. The modular group 43
Previous Page Next Page