The Poincare Conjecture” by Donal O’shea..
Reading Assignment : Chapters 5 and 6 of “The Poincare Conjecture” by Donal O’shea. URL:http://people.math.umass.edu/~franz/Don_OShea_ThePoincareConjecture.pdf : We now had many occassions where we described the 2-sphere as two disks glued along their circle boundary. Use stereographic projection from the north resp. south poles to explain this model of the 2-sphere in terms of two charts (the images of the stereographic projections of the two hemispheres). Calculate explicitely the stereographic projection map and its inverse. Also caclulate the transition function between the two pages of your atlas of the earth: the north pole projection and the south pole projection. You will need to do some research on your own if you haven’t seen the stereographic projection before.