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VOL. 63 | 2012 Harmonic Galois theory for finite graphs
Scott Corry

Editor(s) Hiroaki Nakamura, Florian Pop, Leila Schneps, Akio Tamagawa

## Abstract

This paper develops a harmonic Galois theory for finite graphs, thereby classifying harmonic branched $G$-covers of a fixed base $X$ in terms of homomorphisms from a suitable fundamental group of $X$ together with $G$-inertia structures on $X$. As applications, we show that finite embedding problems for graphs have proper solutions and prove a Grunwald–Wang type result stating that an arbitrary collection of fibers may be realized by a global cover.

## Information

Published: 1 January 2012
First available in Project Euclid: 24 October 2018

zbMATH: 1321.05106
MathSciNet: MR3051241

Digital Object Identifier: 10.2969/aspm/06310121

Subjects:
Primary: 05C25
Secondary: 11R32, 14H30