On hyperbolic cobordisms and Hurwitz classes of holomorphic coverings

Carlos Cabrera; Peter Makienko; Guillermo Sienra

paper

On hyperbolic cobordisms and Hurwitz classes of holomorphic coverings

arXiv:1708.09854

Abstract

In this article we show that for every collection $C$ of an even number of polynomials, all of the same degree $d > 2$ and in general position, there exist two hyperbolic $3$ -orbifolds $M_{1}$ and $M_{2}$ with a Möbius morphism $α : M_{1} \to M_{2}$ such that the restriction of $α$ to the boundaries $\partial M_{1}$ and $\partial M_{2}$ forms a collection of maps $Q$ in the same conformal Hurwitz class of the initial collection $C$ . Also, we discuss the relationship between conformal Hurwitz classes of rational maps and classes of continuous isomorphisms of sandwich products on the set of rational maps.

arXiv comment3 figures, 27 pages