VERTICAL 3-MANIFOLDS IN SIMPLIFIED GENUS-2 TRISECTIONS OF 4-MANIFOLDS

Asano, Nobutaka

doi:https://doi.org/10.18910/88485

VERTICAL 3-MANIFOLDS IN SIMPLIFIED GENUS-2 TRISECTIONS OF 4-MANIFOLDS

Asano, Nobutaka

Osaka Journal of Mathematics, 2022, 59(3), 529-548

アクセス数:79件（2025-07-13 17:49 集計）

固定URL: https://doi.org/10.18910/88485

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タイトル	VERTICAL 3-MANIFOLDS IN SIMPLIFIED GENUS-2 TRISECTIONS OF 4-MANIFOLDS
著者	著者名 Asano, Nobutaka
抄録	We classify the 3-manifolds obtained as the preimages of arcs on the plane for simplified genus-2 trisection maps, which we call vertical 3-manifolds. Vertical 3-manifolds of (2, 1)- and (2, 2)-trisection maps can be easily classified. A vertical 3-manifold of a (2, 0)-trisection map is a connected sum of finite copies of 6-tuple of vertical 3-manifolds over specific 6 arcs and S^1 × S^2. Consequently, we show that each of the 6-tuples determines the source 4-manifold uniquely up to orientation reversing diffeomorphisms except for the trivial case. We also show that, in contrast to the fact that summands of vertical 3-manifolds of simplified (2, 0)-trisection maps are lens spaces, there exist infinitely many simplified (2, 0)-4-section maps that admit hyperbolic vertical 3-manifolds.
出版者	Osaka University and Osaka City University, Departments of Mathematics
収録物名	Osaka Journal of Mathematics
巻(号)	59(3)
ページ	529-548
刊行年月	2022-07
言語	英語
ハンドルURL	https://hdl.handle.net/11094/88485
DOI	https://doi.org/10.18910/88485
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 59, Number 3 （2022-7）

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. 2022, 59(3), p. 529-548
DC.title	VERTICAL 3-MANIFOLDS IN SIMPLIFIED GENUS-2 TRISECTIONS OF 4-MANIFOLDS
DC.creator	Asano, Nobutaka
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	2022-07
DCTERMS.abstract	We classify the 3-manifolds obtained as the preimages of arcs on the plane for simplified genus-2 trisection maps, which we call vertical 3-manifolds. Vertical 3-manifolds of (2, 1)- and (2, 2)-trisection maps can be easily classified. A vertical 3-manifold of a (2, 0)-trisection map is a connected sum of finite copies of 6-tuple of vertical 3-manifolds over specific 6 arcs and S^1 × S^2. Consequently, we show that each of the 6-tuples determines the source 4-manifold uniquely up to orientation reversing diffeomorphisms except for the trivial case. We also show that, in contrast to the fact that summands of vertical 3-manifolds of simplified (2, 0)-trisection maps are lens spaces, there exist infinitely many simplified (2, 0)-4-section maps that admit hyperbolic vertical 3-manifolds.
DC.identifier	10.18910/88485
DC.format	88485
citation_title	VERTICAL 3-MANIFOLDS IN SIMPLIFIED GENUS-2 TRISECTIONS OF 4-MANIFOLDS
citation_author	Asano, Nobutaka
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2022-07
citation_journal_title	Osaka Journal of Mathematics
citation_volume	59
citation_issue	3
citation_firstpage	529
citation_lastpage	548
citation_public_url	https://hdl.handle.net/11094/88485
citation_doi_detail	10.18910/88485
citation_doi	https://doi.org/10.18910/88485

VERTICAL 3-MANIFOLDS IN SIMPLIFIED GENUS-2 TRISECTIONS OF 4-MANIFOLDS

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