About this document
Diffeomorphism Between CP1 and S2 by juanestudia is a document available to read on EtoBox.
This document constructs a diffeomorphism between the complex projective line CP1 and the 2-sphere S2. It does so by defining charts on each space that identify regions with the complex plane C. The transition maps between charts on both spaces are shown to be z → z-1. A map f from CP1 to S2 is then defined by using the charts. This map is proven to be well-defined, smooth, and a diffeomorphism with a smooth inverse.
- Author
- juanestudia
- Language
- EN