On hyperbolic cobordisms and Hurwitz classes of holomorphic coverings

Carlos Cabrera, Peter Makienko, Guillermo Sienra
2019 Conformal Geometry and Dynamics  
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 → M 2 such that the restriction of α to the boundaries ∂M 1 and ∂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
more » ... s of continuous isomorphisms of sandwich products on the set of rational maps.
doi:10.1090/ecgd/345 fatcat:oy47jdqmefhhpmfmnpthy55wl4