On the Riemann-Hurwitz formula for regular graph coverings

On the Riemann-Hurwitz formula for regular graph coverings Full article

Journal

Contemporary Mathematics
ISSN: 0271-4132 , E-ISSN: 1098-3627

Output data

Year: 2022, Volume: 776, Pages: 301-309 Pages count : 9 DOI: 10.1090/conm/776/15618

Tags

Automorphism group; Branched covering; Graph; Harmonic map; Invertible edge; Semi-edge

Authors

Mednykh A. ^1,2,3

Affiliations

1	Tomsk State University, Tomsk, 634050, Russian Federation
2	Sobolev Institute of Mathematics, Novosibirsk, 630090, Russian Federation
3	Department of Mathematics and Mechanics, Novosibirsk State University, Novosibirsk, 630090, Russian Federation

Funding (1)

Russian Science Foundation

19-41-02005

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. © 2022 American Mathematical Society.

Mednykh A.
On the Riemann-Hurwitz formula for regular graph coverings
Contemporary Mathematics. 2022. V.776. P.301-309. DOI: 10.1090/conm/776/15618 Scopus РИНЦ OpenAlex

Scopus:	2-s2.0-85129418226
Elibrary:	48582794
OpenAlex:	W4210686978

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