Directional Invariants of Doubly Periodic Tangles

Ioannis Diamantis; Sofia Lambropoulou; Sonia Mahmoudi

doi:10.3390/sym16080968

Directional Invariants of Doubly Periodic Tangles

Ioannis Diamantis, Sofia Lambropoulou^*, Sonia Mahmoudi

^*Corresponding author for this work

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

Abstract

In this paper, we define novel topological invariants of doubly periodic tangles (DP tangles). DP tangles are embeddings of curves in the thickened plane with translational symmetries in two independent directions. We first organize the components of a DP tangle into different interlinked compounds, which are invariants of a DP tangle. The notion of an interlinked compound leads to the classification of DP tangles according to their directional type. We then prove that the directional type is an invariant of DP tangles using the concept of axis-motif, which can be viewed as the blueprint of a DP tangle.

Original language	English
Article number	968
Journal	Symmetry
Volume	16
Issue number	8
DOIs	https://doi.org/10.3390/sym16080968
Publication status	Published - Aug 2024

Keywords

doubly periodic structures
translational symmetry
tangles
thickened torus
motif
topological invariant
interlinked compound
directional element
directional type
axis-motif

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10.3390/sym16080968Licence: CC BY

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Directional Invariants of Doubly Periodic Tangles
Diamantis, I., Lambropoulou, S. & Mahmoudi, S., 7 Apr 2024, 8 ed., Cornell University - arXiv, 24 p. (arXiv.org; No. 2404.05092).
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title = "Directional Invariants of Doubly Periodic Tangles",

abstract = "In this paper, we define novel topological invariants of doubly periodic tangles (DP tangles). DP tangles are embeddings of curves in the thickened plane with translational symmetries in two independent directions. We first organize the components of a DP tangle into different interlinked compounds, which are invariants of a DP tangle. The notion of an interlinked compound leads to the classification of DP tangles according to their directional type. We then prove that the directional type is an invariant of DP tangles using the concept of axis-motif, which can be viewed as the blueprint of a DP tangle.",

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AU - Mahmoudi, Sonia

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AB - In this paper, we define novel topological invariants of doubly periodic tangles (DP tangles). DP tangles are embeddings of curves in the thickened plane with translational symmetries in two independent directions. We first organize the components of a DP tangle into different interlinked compounds, which are invariants of a DP tangle. The notion of an interlinked compound leads to the classification of DP tangles according to their directional type. We then prove that the directional type is an invariant of DP tangles using the concept of axis-motif, which can be viewed as the blueprint of a DP tangle.

KW - doubly periodic structures

KW - translational symmetry

KW - tangles

KW - thickened torus

KW - motif

KW - topological invariant

KW - interlinked compound

KW - directional element

KW - directional type

KW - axis-motif

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M3 - Article

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VL - 16

JO - Symmetry

JF - Symmetry

IS - 8

M1 - 968

ER -

Directional Invariants of Doubly Periodic Tangles

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Keywords

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Directional Invariants of Doubly Periodic Tangles

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