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Zapiski Nauchnykh Seminarov POMI, 2016, Volume 446, Pages 70–99 (Mi znsl6284)  

Conjugacy classes of reflections of maps

G. A. Jones

School of Mathematics, University of Southampton, Southampton SO17 1BJ, U.K.
References:
Abstract: This paper considers how many conjugacy classes of reflections a map can have, under various transitivity conditions. It is shown that for vertex- and for face-transitive maps there is no restriction on their number or size, whereas edge-transitive maps can have at most four classes of reflections. Examples are constructed, using topology, covering spaces and group theory, to show that various distributions of reflections can be achieved. Connections with real forms of algebraic curves are also discussed.
Key words and phrases: map, reflection vertex-transitive, edge-transitive, conjugacy class, Riemann surface, real form.
Received: 19.10.2015
English version:
Journal of Mathematical Sciences (New York), 2017, Volume 226, Issue 5, Pages 588–607
DOI: https://doi.org/10.1007/s10958-017-3552-8
Bibliographic databases:
Document Type: Article
UDC: 519.175.1+519.146+515.162.6
MSC: Primary 05C10; Secondary 14H37, 14H57, 20B25, 30F10, 30F50
Language: English
Citation: G. A. Jones, “Conjugacy classes of reflections of maps”, Combinatorics and graph theory. Part V, Zap. Nauchn. Sem. POMI, 446, POMI, St. Petersburg, 2016, 70–99; J. Math. Sci. (N. Y.), 226:5 (2017), 588–607
Citation in format AMSBIB
\Bibitem{Jon16}
\by G.~A.~Jones
\paper Conjugacy classes of reflections of maps
\inbook Combinatorics and graph theory. Part~V
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 446
\pages 70--99
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6284}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3520423}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2017
\vol 226
\issue 5
\pages 588--607
\crossref{https://doi.org/10.1007/s10958-017-3552-8}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85029679161}
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  • https://www.mathnet.ru/eng/znsl6284
  • https://www.mathnet.ru/eng/znsl/v446/p70
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