The Dabkowski-Sahi invariant and 4-moves for links

Haruko A. Miyazawa; Kodai Wada; Akira Yasuhara

doi:10.1007/s10711-023-00780-4

The Dabkowski-Sahi invariant and 4-moves for links

Haruko A. Miyazawa, Kodai Wada^*, Akira Yasuhara

^*Corresponding author for this work

School of Commerce

Research output: Contribution to journal › Article › peer-review

Abstract

Dabkowski and Sahi defined an invariant of a link in the 3-sphere, which is preserved under 4-moves. This invariant is a quotient of the fundamental group of the complement of the link. It is generally difficult to distinguish between the Dabkowski-Sahi invariants of given links. In this paper, we give a necessary condition for the existence of an isomorphism between the Dabkowski-Sahi invariant of a link and that of the corresponding trivial link. Using this condition, we provide a practical obstruction to a link to be trivial up to 4-moves.

Original language	English
Article number	46
Journal	Geometriae Dedicata
Volume	217
Issue number	3
DOIs	https://doi.org/10.1007/s10711-023-00780-4
Publication status	Published - 2023 Jun

Keywords

4-move
Link
Link-homotopy
Magnus expansion
Welded link

ASJC Scopus subject areas

Geometry and Topology

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10.1007/s10711-023-00780-4

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title = "The Dabkowski-Sahi invariant and 4-moves for links",

abstract = "Dabkowski and Sahi defined an invariant of a link in the 3-sphere, which is preserved under 4-moves. This invariant is a quotient of the fundamental group of the complement of the link. It is generally difficult to distinguish between the Dabkowski-Sahi invariants of given links. In this paper, we give a necessary condition for the existence of an isomorphism between the Dabkowski-Sahi invariant of a link and that of the corresponding trivial link. Using this condition, we provide a practical obstruction to a link to be trivial up to 4-moves.",

keywords = "4-move, Link, Link-homotopy, Magnus expansion, Welded link",

author = "Miyazawa, {Haruko A.} and Kodai Wada and Akira Yasuhara",

note = "Funding Information: The authors would like to thank the referee for valuable comments on an early version of this paper, and in particular for suggesting us to work on 3-component links, which led to Theorem and Proposition . The second author was supported by JSPS KAKENHI Grant Number JP21K20327. The third author was supported by JSPS KAKENHI Grant Number JP21K03237 and Waseda University Grant for Special Research Projects (Project number: 2021C-120). Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive licence to Springer Nature B.V.",

year = "2023",

month = jun,

doi = "10.1007/s10711-023-00780-4",

language = "English",

volume = "217",

journal = "Geometriae Dedicata",

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T1 - The Dabkowski-Sahi invariant and 4-moves for links

AU - Miyazawa, Haruko A.

AU - Wada, Kodai

AU - Yasuhara, Akira

N1 - Funding Information: The authors would like to thank the referee for valuable comments on an early version of this paper, and in particular for suggesting us to work on 3-component links, which led to Theorem and Proposition . The second author was supported by JSPS KAKENHI Grant Number JP21K20327. The third author was supported by JSPS KAKENHI Grant Number JP21K03237 and Waseda University Grant for Special Research Projects (Project number: 2021C-120). Publisher Copyright: © 2023, The Author(s), under exclusive licence to Springer Nature B.V.

PY - 2023/6

Y1 - 2023/6

N2 - Dabkowski and Sahi defined an invariant of a link in the 3-sphere, which is preserved under 4-moves. This invariant is a quotient of the fundamental group of the complement of the link. It is generally difficult to distinguish between the Dabkowski-Sahi invariants of given links. In this paper, we give a necessary condition for the existence of an isomorphism between the Dabkowski-Sahi invariant of a link and that of the corresponding trivial link. Using this condition, we provide a practical obstruction to a link to be trivial up to 4-moves.

AB - Dabkowski and Sahi defined an invariant of a link in the 3-sphere, which is preserved under 4-moves. This invariant is a quotient of the fundamental group of the complement of the link. It is generally difficult to distinguish between the Dabkowski-Sahi invariants of given links. In this paper, we give a necessary condition for the existence of an isomorphism between the Dabkowski-Sahi invariant of a link and that of the corresponding trivial link. Using this condition, we provide a practical obstruction to a link to be trivial up to 4-moves.

KW - 4-move

KW - Link

KW - Link-homotopy

KW - Magnus expansion

KW - Welded link

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DO - 10.1007/s10711-023-00780-4

M3 - Article

AN - SCOPUS:85149003647

SN - 0046-5755

VL - 217

JO - Geometriae Dedicata

JF - Geometriae Dedicata

IS - 3

M1 - 46

ER -

The Dabkowski-Sahi invariant and 4-moves for links

Abstract

Keywords

ASJC Scopus subject areas

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