ON AUTOMORPHISMS OF KLEIN SURFACES WITH INVARIANT SUBSETS

Bujalance, E.; Gromadzki, G.

doi:https://doi.org/10.18910/24482

このアイテムのアクセス数:95件（2023-10-03 02:18 集計）

このアイテムへのリンクには次のURLをご利用ください: https://doi.org/10.18910/24482

このアイテムへのリンクには次のURLをご利用ください: https://hdl.handle.net/11094/24482

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タイトル	ON AUTOMORPHISMS OF KLEIN SURFACES WITH INVARIANT SUBSETS
著者	著者名 Bujalance, E.
著者	著者名 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.
出版者	Osaka University and Osaka City University, Departments of Mathematics
収録物名	Osaka Journal of Mathematics
巻(号)	50(1)
ページ	251-269
刊行年月	2013-03
言語	英語
ハンドルURL	https://hdl.handle.net/11094/24482
DOI	https://doi.org/10.18910/24482
PISSN	00306126
NCID	AA00765910
アクセス権	open access
出版タイプ	Version of Record
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）

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. 2013, 50(1), p. 251-269
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
DC.type' scheme='DCTERMS.DCMIType	text
DCTERMS.issued' scheme='DCTERMS.W3CDTF	2013-03
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	10.18910/24482
DC.format	application/pdf
citation_doi	https://doi.org/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_public_url	https://hdl.handle.net/11094/24482
citation_doi_detail	10.18910/24482

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