Year: 2026
Type: preprint
Abstract: We study the functional equation $ f \circ p = g \circ q,$ where $ f,$ $g,$ $p,$ $q$ are branched covering maps between closed surfaces. In particular, we extend results on semiconjugate holomorphic maps between compact Riemann surfaces to this broader setting. As an application, we present an alternative proof of the fact that every quotient of a torus endomorphism has a parabolic orbifold, along with some extensions of this result.
Source: arXiv (Cornell University)
Author: Pakovich, Fedor
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Israel Science Foundation
Award: G1573168548
OpenAlex ID: W7214008059