ON AUTOMORPHISMS OF KLEIN SURFACES WITH INVARIANT SUBSETS

Bujalance, E.; Gromadzki, G.

doi:info:doi/10.18910/24482

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タイトル	ON AUTOMORPHISMS OF KLEIN SURFACES WITH INVARIANT SUBSETS
著者	Bujalance, E. Bujalance, E.
著者	Gromadzki, G. Gromadzki, G.
抄録	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.
公開者	Osaka University and Osaka City University, Departments of Mathematics
掲載誌名	Osaka Journal of Mathematics
巻	50
号	1
開始ページ	251
終了ページ	269
刊行年月	2013-03
ISSN	00306126
NCID	AA00765910
URL	http://hdl.handle.net/11094/24482
言語	英語
DOI	info:doi/10.18910/24482
カテゴリ	紀要論文 Departmental Bulletin Paper
カテゴリ	Osaka Journal of Mathematics / Volume 50, Number 1　(2013-3）

著者版フラグ	publisher
NII資源タイプ	紀要論文
ローカル資源タイプ	紀要論文
dcmi資源タイプ	text
DCTERMS.bibliographicCitation	Osaka Journal of Mathematics.50(1) P.251-P.269
DC.title	ON AUTOMORPHISMS OF KLEIN SURFACES WITH INVARIANT SUBSETS
DC.creator	Bujalance, E.
DC.creator	Gromadzki, G.
DC.publisher	Osaka University and Osaka City University, Departments of Mathematics
DC.language" scheme="DCTERMS.RFC1766	英語
DCTERMS.issued" scheme="DCTERMS.W3CDTF	2013-03
DC.identifier" scheme="DCTERMS.URI	http://hdl.handle.net/11094/24482
DCTERMS.abstract	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.
DC.identifier	info:doi/10.18910/24482
citation_title	ON AUTOMORPHISMS OF KLEIN SURFACES WITH INVARIANT SUBSETS
citation_author	Bujalance, E.
citation_author	Gromadzki, G.
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2013-03
citation_journal_title	Osaka Journal of Mathematics
citation_volume	50
citation_issue	1
citation_firstpage	251
citation_lastpage	269
citation_issn	00306126
citation_public_url	http://hdl.handle.net/11094/24482
citation_doi	info:doi/10.18910/24482

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