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On the Riemann-Hurwitz formula for regular graph coverings. / Mednykh, Alexander.
в: Contemporary Mathematics, Том 776, 14, 2022, стр. 301-309.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - On the Riemann-Hurwitz formula for regular graph coverings
AU - Mednykh, Alexander
N1 - Funding Information: 2020 Mathematics Subject Classification. Primary 30F40, 20H10; Secondary 14E20, 14H30. Key words and phrases. graph, semi-edge, invertible edge, branched covering, automorphism group, harmonic map. The author was supported by the Russian Science Foundation (grant 19-41-02005). Publisher Copyright: © 2022 American Mathematical Society.
PY - 2022
Y1 - 2022
N2 - The aim of this paper is to present a few versions of the Riemann-Hurwitz formula for a regular branched covering of graphs. By a graph, we mean a finite connected multigraph. The genus of a graph is defined as the rank of the first homology group. We consider a finite group acting on a graph, possibly with fixed and invertible edges, and the respective factor graph. Then, the obtained Riemann-Hurwitz formula relates genus of the graph with genus of the factor graph and orders of the vertex and edge stabilizers.
AB - The aim of this paper is to present a few versions of the Riemann-Hurwitz formula for a regular branched covering of graphs. By a graph, we mean a finite connected multigraph. The genus of a graph is defined as the rank of the first homology group. We consider a finite group acting on a graph, possibly with fixed and invertible edges, and the respective factor graph. Then, the obtained Riemann-Hurwitz formula relates genus of the graph with genus of the factor graph and orders of the vertex and edge stabilizers.
KW - Automorphism group
KW - Branched covering
KW - Graph
KW - Harmonic map
KW - Invertible edge
KW - Semi-edge
UR - http://www.scopus.com/inward/record.url?scp=85129418226&partnerID=8YFLogxK
UR - https://www.mendeley.com/catalogue/e314dd8d-4821-3362-9469-1227b06c5e04/
U2 - 10.1090/conm/776/15618
DO - 10.1090/conm/776/15618
M3 - Article
AN - SCOPUS:85129418226
VL - 776
SP - 301
EP - 309
JO - Contemporary Mathematics
JF - Contemporary Mathematics
SN - 0271-4132
M1 - 14
ER -
ID: 36060597