RT Book, Section
T1 On the minimum genus problem on bordered Klein surfaces for automorphisms of even order
A1 Etayo Gordejuela, José Javier
A1 Martínez García, Ernesto
A2 Izquierdo, Milagros
A2 Broughton, S. Allen
A2 Costa, Antonio F.
A2 Rodríguez, Rubí E.
AB The minimum genus problem consists on determining the minimum algebraic genus of a surface on which a given group G acts. For cyclic groups G this problem on bordered Klein surfaces was solved in 1989. The next step is to fix the number of boundary components of the surface and to obtain the minimum algebraic genus, and so the minimum topological genus. It was achieved for cyclic groups of prime and prime-power order in the nineties. In this work the corresponding results for cyclic groups of order N = 2q, where q is an odd prime, are obtained. There appear different results depending on the orientability of the surface. Finally, using the above mentioned results and those of this paper, we state explicitly, the general values for arbitrary number of boundary components, which are valid for each N < 12, and show how to deal with N = 12.
PB American Mathematical Society
SN 978-1-4704-1093-3
YR 2014
FD 2014
LK https://hdl.handle.net/20.500.14352/35791
UL https://hdl.handle.net/20.500.14352/35791
NO Etayo Gordejuela, J. J. & Martínez García, E. Riemann and Klein Surfaces, Automorphisms, Symmetries and Moduli Spaces. American Mathematical Society, 2014. DOI.org (Crossref), https://doi.org/10.1090/conm/629.
NO Proceedings of the conference on Riemann and Klein Surfaces, Symmetries and Moduli Spaces, in honor of Emilio Bujalance, held from June 24–28, 2013, at Linköping University, Sweden
DS Docta Complutense
RD 26 feb 2026