This article is cited in 2 papers

Real, complex and functional analysis

Non-regular graph coverings and lifting the hyperelliptic involution

Maxim P. Limonov<sup>abc

a</sup> Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
^b Laboratory of Quantum Topology, Chelyabinsk State University, Br. Kashirinykh str., 129, room 419, 430, 454001, Chelyabinsk, Russia
^c Novosibirsk State University, Pirogova st. 2, 630090, Novosibirsk, Russia

Abstract: In this paper, we prove that there exists a non-regular hyperelliptic covering of any odd degree over a hyperelliptic graph. Also, some properties of a dihedral covering, with a rotation being of odd degree, over a genus two hyperelliptic graph are derived. In the proof, the Bass–Serre theory is employed.

Keywords: Riemann surface, graph, hyperelliptic graph, hyperelliptic involution, fundamental group, automorphism group, harmonic map, branched covering, non-regular covering, graph of groups.

UDC: 519.173+517.545

MSC: 05C10+57M12

Received June 2, 2015, published June 9, 2015

Language: English

DOI: 10.17377/semi.2015.12.031