Maps of complex hyperbolic surfaces

 

 

Domingo Toledo

U. Utah, USA

 


Abstract

We study a class of examples of surjective holomorphic maps between compact two-dimensional ball quotients that are not covering maps.  We find all such maps that can be written in terms of hypergeometric functions.  They have the property that the induced homomorphism in fundamental groups is not injective.  They include Mostow's example of a non-injective homomorphism, and are motivated by that example.  We study the singularity behavior of these maps, and state a number of natural problems that are suggested by these examples.