FUKAYA CATEGORY OF INFINITE-TYPE SURFACES

Choi, Jaeyoung; Oh, Yong-Geun

doi:https://doi.org/10.18910/97641

FUKAYA CATEGORY OF INFINITE-TYPE SURFACES

Choi, Jaeyoung; Oh, Yong-Geun

Osaka Journal of Mathematics, 2024, 61(3), 419-465

アクセス数:52件（2025-03-22 05:05 集計）

固定URL: https://doi.org/10.18910/97641

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タイトル	FUKAYA CATEGORY OF INFINITE-TYPE SURFACES
著者	著者名 Choi, Jaeyoung
著者	著者名 Oh, Yong-Geun
抄録	In this paper, we construct a Fukaya category of any infinite type surface whose objects are gradient sectorial Lagrangians. This class of Lagrangian submanifolds is introduced by one of the authors in which can serve as an object of a Fukaya category of any Liouville manifold that admits an exhausting properMorse function, in particular on the Riemann surface of infinite type. We describe a generating set of the Fukaya category in terms of the end structure of the surface when the surface has countably many limit points in its ideal boundary, the latter of which can be described in terms of a subset of the Cantor set. We also show that our Fukaya category is not quasi-equivalent to the limit of the Fukaya category of surfaces of finite type appearing in the literature.
出版者	Osaka University and Osaka City University, Departments of Mathematics
収録物名	Osaka Journal of Mathematics
巻(号)	61(3)
ページ	419-465
刊行年月	2024-07
言語	英語
ハンドルURL	https://hdl.handle.net/11094/97641
DOI	https://doi.org/10.18910/97641
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 61, Number 3 （2024-07）

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. 2024, 61(3), p. 419-465
DC.title	FUKAYA CATEGORY OF INFINITE-TYPE SURFACES
DC.creator	Choi, Jaeyoung
DC.creator	Oh, Yong-Geun
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	2024-07
DCTERMS.abstract	In this paper, we construct a Fukaya category of any infinite type surface whose objects are gradient sectorial Lagrangians. This class of Lagrangian submanifolds is introduced by one of the authors in which can serve as an object of a Fukaya category of any Liouville manifold that admits an exhausting properMorse function, in particular on the Riemann surface of infinite type. We describe a generating set of the Fukaya category in terms of the end structure of the surface when the surface has countably many limit points in its ideal boundary, the latter of which can be described in terms of a subset of the Cantor set. We also show that our Fukaya category is not quasi-equivalent to the limit of the Fukaya category of surfaces of finite type appearing in the literature.
DC.identifier	10.18910/97641
DC.format	97641
citation_title	FUKAYA CATEGORY OF INFINITE-TYPE SURFACES
citation_author	Choi, Jaeyoung
citation_author	Oh, Yong-Geun
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2024-07
citation_journal_title	Osaka Journal of Mathematics
citation_volume	61
citation_issue	3
citation_firstpage	419
citation_lastpage	465
citation_public_url	https://hdl.handle.net/11094/97641
citation_doi_detail	10.18910/97641
citation_doi	https://doi.org/10.18910/97641

FUKAYA CATEGORY OF INFINITE-TYPE SURFACES

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