A prime decomposition theorem for string links in a thickened surface

We prove a prime decomposition theorem for string links in a thickened surface. Namely, we prove that any non-braid string link [Formula: see text], where [Formula: see text] is a compact orientable (not necessarily closed) surface other than [Formula: see text], can be written in the form [Formula: see text], where [Formula: see text] is prime string link defined up to braid equivalence, and the decomposition is unique up to possibly permuting the order of factors in its right-hand side.

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Publication Details

Journal
Journal of Knot Theory and Its Ramifications
Published
2024-10-11
DOI
https://doi.org/10.1142/s021821652450041x
Primary Topic
Contact Mechanics and Variational Inequalities
Type
article
Field-Weighted Citation Impact
0.00

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article

A prime decomposition theorem for string links in a thickened surface

Vladimir Tarkaev
Journal of Knot Theory and Its Ramifications
Contact Mechanics and Variational Inequalities
article

A prime decomposition theorem for string links in a thickened surface

Vladimir Tarkaev
article en

Abstract

We prove a prime decomposition theorem for string links in a thickened surface. Namely, we prove that any non-braid string link [Formula: see text], where [Formula: see text] is a compact orientable (not necessarily closed) surface other than [Formula: see text], can be written in the form [Formula: see text], where [Formula: see text] is prime string link defined up to braid equivalence, and the decomposition is unique up to possibly permuting the order of factors in its right-hand side.

Journal of Knot Theory and Its RamificationsVol. 33(13)
Russian Academy of Sciences (RU), Chelyabinsk State University (RU), Steklov Mathematical Institute (RU), N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences (RU), Ural Branch of the Russian Academy of Sciences (RU)
Russian Science Foundation
Openalex Percentile: Top 79%
Contact Mechanics and Variational Inequalities
DOISourceOpenAlex
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A prime decomposition theorem for string links in a thickened surface — Vladimir Tarkaev · Journal of Knot Theory and Its Ramifications (2024) | TGRS Research Map | TGRS