TWO-TONE COLORINGS AND SURJECTIVE DIHEDRAL REPRESENTATIONS FOR LINKS

Ichihara, Kazuhiro; Ishikawa, Katsumi; Matsudo, Eri; Suzuki, Masaaki

doi:https://doi.org/10.18910/102430

TWO-TONE COLORINGS AND SURJECTIVE DIHEDRAL REPRESENTATIONS FOR LINKS

Ichihara, Kazuhiro; Ishikawa, Katsumi; Matsudo, Eri et al.

Osaka Journal of Mathematics, 2025, 62(3), 381-393

アクセス数:101件（2026-02-10 16:42 集計）

固定URL: https://doi.org/10.18910/102430

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タイトル	TWO-TONE COLORINGS AND SURJECTIVE DIHEDRAL REPRESENTATIONS FOR LINKS
著者	NRID 1000000388357 1000000388357 著者名 Ichihara, Kazuhiro
	NRID 1000090850610 1000090850610 著者名 Ishikawa, Katsumi
	著者名 Matsudo, Eri
	NRID 1000070431616 1000070431616 著者名 Suzuki, Masaaki
抄録	It is well-known that a knot is Fox n-colorable for a prime n if and only if the knot group admits a surjective homomorphism to the dihedral group of degree n. However, this is not the case for links with two or more components. In this paper, we introduce a two-tone coloring on a link diagram, and give a condition for links so that the link groups admit surjective representations to the dihedral groups. In particular, it is shown that the link group of any link with at least 3 components admits a surjective homomorphism to the dihedral group of arbitrary degree.
出版者	Departments of Mathematics, The University of Osaka and Osaka Metropolitan University
収録物名	Osaka Journal of Mathematics
巻(号)	62(3)
ページ	381-393
刊行年月	2025-07
言語	英語
ハンドルURL	https://hdl.handle.net/11094/102430
DOI	https://doi.org/10.18910/102430
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 62, Number 3 （2025-07）

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. 2025, 62(3), p. 381-393
DC.title	TWO-TONE COLORINGS AND SURJECTIVE DIHEDRAL REPRESENTATIONS FOR LINKS
DC.creator	Ichihara, Kazuhiro
	Ishikawa, Katsumi
	Matsudo, Eri
	Suzuki, Masaaki
DC.publisher	Departments of Mathematics, The University of Osaka and Osaka Metropolitan University
DC.language' scheme='DCTERMS.RFC1766	英語
DC.type' scheme='DCTERMS.DCMIType	text
DCTERMS.issued' scheme='DCTERMS.W3CDTF	2025-07
DCTERMS.abstract	It is well-known that a knot is Fox n-colorable for a prime n if and only if the knot group admits a surjective homomorphism to the dihedral group of degree n. However, this is not the case for links with two or more components. In this paper, we introduce a two-tone coloring on a link diagram, and give a condition for links so that the link groups admit surjective representations to the dihedral groups. In particular, it is shown that the link group of any link with at least 3 components admits a surjective homomorphism to the dihedral group of arbitrary degree.
DC.identifier	10.18910/102430
DC.format	102430
citation_title	TWO-TONE COLORINGS AND SURJECTIVE DIHEDRAL REPRESENTATIONS FOR LINKS
citation_author	Ichihara, Kazuhiro
	Ishikawa, Katsumi
	Matsudo, Eri
	Suzuki, Masaaki
citation_publisher	Departments of Mathematics, The University of Osaka and Osaka Metropolitan University
citation_language	英語
citation_date	2025-07
citation_journal_title	Osaka Journal of Mathematics
citation_volume	62
citation_issue	3
citation_firstpage	381
citation_lastpage	393
citation_public_url	https://hdl.handle.net/11094/102430
citation_doi_detail	10.18910/102430
citation_doi	https://doi.org/10.18910/102430

TWO-TONE COLORINGS AND SURJECTIVE DIHEDRAL REPRESENTATIONS FOR LINKS

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