FIXED POINTS OF CYCLIC GROUPS ACTING PURELY HARMONICALLY ON A GRAPH | Sciact - Система учета научной деятельности ИМ СО РАН

FIXED POINTS OF CYCLIC GROUPS ACTING PURELY HARMONICALLY ON A GRAPH Научная публикация

Журнал

Сибирские электронные математические известия (Siberian Electronic Mathematical Reports)
, E-ISSN: 1813-3304

Вых. Данные

Год: 2021, Том: 18, Номер: 1, Страницы: 617-621 Страниц : 5 DOI: 10.33048/semi.2021.18.044

Ключевые слова

fixed point; graph; harmonic automorphism; homological genus; Wiman theorem

Авторы

Mednykh A.D. ^1,2

Организации

1	Sobolev Institute of Mathematics 4, KOPTYUGA AVE., Novosibirsk, 30090, Russian Federation
2	Novosibirsk State University, 1, Pirogova str., Novosibirsk, 630090, Russia

Информация о финансировании (1)

Институт математики им. С.Л. Соболева СО РАН

0314-2019-0007

Let X be a finite connected graph, possibly with loops and multiple edges. An automorphism group of X acts purely harmonically if it acts freely on the set of directed edges of X and has no invertible edges. Define a genus g of the graph X to be the rank of the first homology group. A discrete version of the Wiman theorem states that the order of a cyclic group ℤn acting purely harmonically on a graph X of genus g > 1 is bounded from above by 2g + 2. In the present paper, we investigate how many fixed points has an automorphism generating a «large» cyclic group ℤn of order n > 2g — 1. We show that in the most cases, the automorphism acts fixed point free, while for groups of order 2g and 2g — 1 it can have one or two fixed points. © 2021 Mednykh A.D. All Rights Reserved.

Mednykh A.D.
FIXED POINTS OF CYCLIC GROUPS ACTING PURELY HARMONICALLY ON A GRAPH
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2021. V.18. N1. P.617-621. DOI: 10.33048/semi.2021.18.044 WOS Scopus OpenAlex

Web of science:	WOS:000674348900001
Scopus:	2-s2.0-85108826330
OpenAlex:	W3200244531

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