RT Journal Article
T1 The action of the groups Dm × Dn  on unbordered Klein surfaces
A1 Etayo Gordejuela, José Javier
A1 Martínez García, Ernesto
AB Every finite group G may act as an automorphism group of Klein surfaces either bordered or unbordered either orientable or non-orientable. For each group the minimum genus receives different names according to the topological features of the surface X on which it acts. If X is a bordered surface the genus is called the real genus ρ(G). If X is a non-orientable unbordered surface the genus is called the symmetric crosscap number of G and it is denoted by [(s)\tilde](G)(G). Finally if X is a Riemann surface it has two related parameters. If G only contains orientation-preserving automorphisms we have the strong symmetric genus, σ 0(G). If we allow orientation-reversing automorphisms we have the symmetric genus σ(G). In this work we obtain the strong symmetric genus and the symmetric crosscap number of the groups D m  × D n . The symmetric genus of these groups is 1. However we introduce and obtain a new parameter, denoted by τ as the least genus g ≥ 2 of Riemann surfaces on which these groups act disregarding orientation
PB Springer
SN 1578-7303
YR 2011
FD 2011
LK https://hdl.handle.net/20.500.14352/42221
UL https://hdl.handle.net/20.500.14352/42221
LA eng
NO Etayo Gordejuela, J. J., & Martínez García, E. «The Action of the Groups D m × D n on Unbordered Klein Surfaces». Revista de La Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, vol. 105, n.o 1, marzo de 2011, pp. 97-108. DOI.org (Crossref), https://doi.org/10.1007/s13398-011-0007-9.
DS Docta Complutense
RD 21 abr 2025