On the minimum genus problem on bordered Klein surfaces for automorphisms of even order



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Etayo Gordejuela, J. Javier and Martínez, E. (2014) On the minimum genus problem on bordered Klein surfaces for automorphisms of even order. In Riemann and Klein Surfaces, Automorphisms, Symmetries and Moduli Spaces. Contemporary mathematics, 629 . American Mathematical Society, Providence, Rhode Island, pp. 119-135. ISBN 978-1-4704-1093-3

Official URL: http://www.ams.org/books/conm/629/


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.

Item Type:Book Section
Additional Information:

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

Uncontrolled Keywords:Klein surfaces; algebraic genus; boundary components
Subjects:Sciences > Mathematics > Functions
Sciences > Mathematics > Group Theory
ID Code:34478
Deposited On:01 Dec 2015 08:44
Last Modified:01 Dec 2015 08:44

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