ON CALCULATIONS OF THE TWISTED ALEXANDER IDEALS FOR SPATIAL GRAPHS, HANDLEBODY-KNOTS AND SURFACE-LINKS

Ishii, Atsushi; Nikkuni, Ryo; Oshiro, Kanako

doi:https://doi.org/10.18910/68353

アクセス数:157件（2024-11-09 08:51 集計）

固定URL: https://doi.org/10.18910/68353

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タイトル	ON CALCULATIONS OF THE TWISTED ALEXANDER IDEALS FOR SPATIAL GRAPHS, HANDLEBODY-KNOTS AND SURFACE-LINKS
著者	NRID 1000000531451 1000000531451 著者名 Ishii, Atsushi
	NRID 1000000401878 1000000401878 著者名 Nikkuni, Ryo
	NRID 1000090609091 1000090609091 著者名 Oshiro, Kanako
抄録	There are many studies about twisted Alexander invariants for knots and links, but calculations of twisted Alexander invariants for spatial graphs, handlebody-knots, and surface-links have not been demonstrated well. In this paper, we give some remarks to calculate the twisted Alexander ideals for spatial graphs, handlebody-knots and surface-links, and observe their behaviors. For spatial graphs, we calculate the invariants of Suzuki’s theta-curves and show that the invariants are nontrivial for Suzuki’s theta-curves whose Alexander ideals are trivial. For handlebodyknots, we give a remark on abelianizations and calculate the invariant of the handlebody-knots up to six crossings. For surface-links, we correct Yoshikawa’s table and calculate the invariants of the surface-links in the table.
出版者	Osaka University and Osaka City University, Departments of Mathematics
収録物名	Osaka Journal of Mathematics
巻(号)	55(2)
ページ	297-313
刊行年月	2018-04
言語	英語
ハンドルURL	https://hdl.handle.net/11094/68353
DOI	https://doi.org/10.18910/68353
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 55, Number 2 （2018-4）

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. 2018, 55(2), p. 297-313
DC.title	ON CALCULATIONS OF THE TWISTED ALEXANDER IDEALS FOR SPATIAL GRAPHS, HANDLEBODY-KNOTS AND SURFACE-LINKS
DC.creator	Ishii, Atsushi
	Nikkuni, Ryo
	Oshiro, Kanako
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	2018-04
DCTERMS.abstract	There are many studies about twisted Alexander invariants for knots and links, but calculations of twisted Alexander invariants for spatial graphs, handlebody-knots, and surface-links have not been demonstrated well. In this paper, we give some remarks to calculate the twisted Alexander ideals for spatial graphs, handlebody-knots and surface-links, and observe their behaviors. For spatial graphs, we calculate the invariants of Suzuki’s theta-curves and show that the invariants are nontrivial for Suzuki’s theta-curves whose Alexander ideals are trivial. For handlebodyknots, we give a remark on abelianizations and calculate the invariant of the handlebody-knots up to six crossings. For surface-links, we correct Yoshikawa’s table and calculate the invariants of the surface-links in the table.
DC.identifier	10.18910/68353
DC.format	68353
citation_title	ON CALCULATIONS OF THE TWISTED ALEXANDER IDEALS FOR SPATIAL GRAPHS, HANDLEBODY-KNOTS AND SURFACE-LINKS
citation_author	Ishii, Atsushi
	Nikkuni, Ryo
	Oshiro, Kanako
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2018-04
citation_journal_title	Osaka Journal of Mathematics
citation_volume	55
citation_issue	2
citation_firstpage	297
citation_lastpage	313
citation_public_url	https://hdl.handle.net/11094/68353
citation_doi_detail	10.18910/68353
citation_doi	https://doi.org/10.18910/68353

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