Abstract
An important problem in the study of Riemann and Klein surfaces is determining their full automorphism groups. Up to now only very partial results are known, concerning surfaces of low genus or families of surfaces with special properties. This paper deals with non-orientable unbordered Klein surfaces. In this case the solution of the problem is known for surfaces of genus 1 and 2, and for hyperelliptic surfaces. Here we explicitly obtain the full automorphism group of all surfaces of genus 3, 4 and 5.
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The authors wish to express their deep gratitude to the referee for the careful checking of the manuscript and for the very useful suggestions concerning both the style and the precision of arguments.
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The authors wish to dedicate this paper to the memory of Professor José Javier Etayo (1926–2012). He was our teacher, as well as of many thousands of students throughout forty years in the Universidad Complutense.
E. Bujalance and E. Martínez are partially supported by MTM2011-23092 and J. J. Etayo by UCM910444 and MTM2011-22435.
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Bujalance, E., Etayo, J.J. & Martínez, E. The full group of automorphisms of non-orientable unbordered Klein surfaces of topological genus 3, 4 and 5. Rev Mat Complut 27, 305–326 (2014). https://doi.org/10.1007/s13163-013-0121-7
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DOI: https://doi.org/10.1007/s13163-013-0121-7