A complete invariant for connected surfaces in the 3-sphere

Maurizio Paolini; Giovanni Bellettini; Yi-Sheng Wang

doi:10.1142/S0218216519500913

A complete invariant for connected surfaces in the 3-sphere

Maurizio Paolini, Giovanni Bellettini, Yi-Sheng Wang

Risultato della ricerca: Contributo in rivista › Articolo in rivista › peer review

Abstract

We construct a complete invariant of oriented connected closed surfaces in 3, which generalizes the notion of peripheral system of a knot group. As an application, we define two computable invariants to investigate handlebody knots and bi-knotted surfaces with homeomorphic complements. In particular, we obtain an alternative proof of inequivalence of Ishii, Kishimoto, Moriuchi and Suzuki's handlebody knots 51 and 64.

Lingua originale	English
pagine (da-a)	1-24
Numero di pagine	24
Rivista	Journal of Knot Theory and its Ramifications
Volume	29
DOI	https://doi.org/10.1142/S0218216519500913
Stato di pubblicazione	Pubblicato - 2020

Keywords

Complete invariant
Handlebody knots
Surfaces in the 3-sphere

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10.1142/S0218216519500913

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AU - Bellettini, Giovanni

AU - Wang, Yi-Sheng

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N2 - We construct a complete invariant of oriented connected closed surfaces in 3, which generalizes the notion of peripheral system of a knot group. As an application, we define two computable invariants to investigate handlebody knots and bi-knotted surfaces with homeomorphic complements. In particular, we obtain an alternative proof of inequivalence of Ishii, Kishimoto, Moriuchi and Suzuki's handlebody knots 51 and 64.

AB - We construct a complete invariant of oriented connected closed surfaces in 3, which generalizes the notion of peripheral system of a knot group. As an application, we define two computable invariants to investigate handlebody knots and bi-knotted surfaces with homeomorphic complements. In particular, we obtain an alternative proof of inequivalence of Ishii, Kishimoto, Moriuchi and Suzuki's handlebody knots 51 and 64.

KW - Complete invariant

KW - Handlebody knots

KW - Surfaces in the 3-sphere

KW - Complete invariant

KW - Handlebody knots

KW - Surfaces in the 3-sphere

UR - http://hdl.handle.net/10807/164839

U2 - 10.1142/S0218216519500913

DO - 10.1142/S0218216519500913

M3 - Article

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SP - 1

EP - 24

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

SN - 0218-2165

ER -

A complete invariant for connected surfaces in the 3-sphere

Abstract

Keywords

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