Week 37

The theme this week has been the study of geometric properties of Mõbius transformations.  The goal is to obtain a small number of "normal forms" which makes the geometry transparent and represent all Mõbius transformations up to conjugacy.  This will be concluded next time, and then we are ready to prove that we have an example of Hyperbolic geometry.

Note that there is a misprint at the end of the second paragraph, page 34: the appropriate interval sould be (0,Π/2], and not (0,Π/2).

Exercises for Sep.16: 2.3.1, 4, 5, 6