Smooth transition map (easy!?) 1. The problem statement, all variables and given/known data Check the transition map http://img132.imageshack.us/img132/4341/18142532.png [Broken] is smooth in the set for which their images intersect 3. The attempt at a solution I have thought of two ways to show this. (1) Show that Φ is a composition of two smooth functions and is therefore smooth. (2) compute the composite function and then prove that is smooth Which way do you suggest? I have attempted method (1) to some extent, but wondering if method (2) is easier.