Accola theorem on hyperelliptic graphs

Maxim P. Limonov

Abstract


In this paper, we prove the following theorem:
If a graph X is a degree 2 (unramified) covering of a hyperelliptic graph of genus g >= 2, then X is gamma-hyperelliptic for some gamma <= [(g-1)/2]. This is a discrete analogue of the corresponding theorem for Riemann surfaces. The Bass-Serre theory of coverings of graphs of groups is employed to get the main result.

Keywords


Riemann surface, graph, hyperelliptic graph, fundamental group, automorphism group, harmonic map, branched covering, graph of groups

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DOI: https://doi.org/10.26493/1855-3974.790.202

ISSN: 1855-3974

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