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March 2013 On automorphisms of Klein surfaces with invariant subsets
E. Bujalance, G. Gromadzki
Osaka J. Math. 50(1): 251-269 (March 2013).


It is well known that a group of automorphisms $G$ of an unbordered Klein surface $X$ of topological genus $g\geq 2$ in the orientable case and $g\geq 3$ otherwise has at most $84(g-\varepsilon)$ elements, where $\varepsilon =1$ or $2$ respectively. In the middle of the fifties, Oikawa used the cardinality $k$ of a $G$-invariant subset to introduce the bound $\lvert G\rvert \leq 12(g-1)+6k$ in the orientable case. Much later, T. Arakawa has generalized this result, involving $s=2$ or $3$ such subsets and showing in addition that the bound for $s=3$ is sharp for infinitely many configurations. Here we improve the bound of Arakawa for $s=2$, showing in particular that the last is never attained. In both orientable and non-orientable case, we also find bounds for arbitrary $s$ and show their sharpness for infinitely many topological configurations. Using another well known theorem of Oikawa and the canonical Riemann double cover, we get similar results for bordered Klein surfaces.


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E. Bujalance. G. Gromadzki. "On automorphisms of Klein surfaces with invariant subsets." Osaka J. Math. 50 (1) 251 - 269, March 2013.


Published: March 2013
First available in Project Euclid: 27 March 2013

zbMATH: 1271.30014
MathSciNet: MR3080639

Primary: 30F10 , 30F35 , 30F50
Secondary: 14H37 , 14H45 , 14H55

Rights: Copyright © 2013 Osaka University and Osaka City University, Departments of Mathematics


Vol.50 • No. 1 • March 2013
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