紀要論文

紀要論文

text

Osaka Journal of Mathematics. 2013, 50(1), p. 251-269

ON AUTOMORPHISMS OF KLEIN SURFACES WITH INVARIANT SUBSETS

Osaka University and Osaka City University, Departments of Mathematics

英語

text

2013-03

It is well known that a group of automorphisms G of an unbordered Klein surface X of topological genus g ≥ 2 in the orientable case and g ≥3 otherwise has at most 84(g 􀀀 ") elements, where " D 1 or 2 respectively. In the middle of the fifties, Oikawa used the cardinality k of a G-invariant subset to introduce the bound |G|≤12 (g- 1) C 6k in the orientable case. Much later, T. Arakawa has generalized this result, involving s D 2 or 3 such subsets and showing in addition that the bound for s D 3 is sharp for infinitely many configurations. Here we improve the bound of Arakawa for s D 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.

10.18910/24482

24482

ON AUTOMORPHISMS OF KLEIN SURFACES WITH INVARIANT SUBSETS

Osaka University and Osaka City University, Departments of Mathematics

英語

2013-03

Osaka Journal of Mathematics

50

1

251

269

https://hdl.handle.net/11094/24482

10.18910/24482

https://doi.org/10.18910/24482