Tessellations on surfaces from complex analytic functions

Jesús Muciño Raymundo

UNAM-Morelia (México)

Abstract:

We describe the topology and geometry of complex analytic functions in one variable. In order to perform it, we associate a tessellation of the Riemann sphere to each function. This method allow us to describe complex polynomial, rational and even transcendental functions.

The method has its roots in the pioneering work of F. Klein, and remains as a current subject in several studies.

As one example, we consider a recent question by W. Thurston.