Directional Invariants of Doubly Periodic Tangles

Ioannis Diamantis; Sofia Lambropoulou; Sonia Mahmoudi

doi:10.48550/arXiv.2404.05092

Directional Invariants of Doubly Periodic Tangles

Ioannis Diamantis, Sofia Lambropoulou, Sonia Mahmoudi

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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 that are repeated periodically in two directions. We first organize the components of a DP tangle into different it interlinked compounds, which are invariants of a DP tangle. The notion of interlinked compound leads to the classification of DP tangles according to their it 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
Publisher	Cornell University - arXiv
Number of pages	24
DOIs	https://doi.org/10.48550/arXiv.2404.05092
Publication status	Published - 7 Apr 2024

Publication series

Series	arXiv.org
Number	2404.05092
ISSN	2331-8422

Keywords

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

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http://adsabs.harvard.edu/abs/2024arXiv240405092D

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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 that are repeated periodically in two directions. We first organize the components of a DP tangle into different it interlinked compounds, which are invariants of a DP tangle. The notion of interlinked compound leads to the classification of DP tangles according to their it 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 - Lambropoulou, Sofia

AU - Mahmoudi, Sonia

PY - 2024/4/7

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N2 - In this paper we define novel topological invariants of doubly periodic tangles (DP tangles). DP tangles are embeddings of curves in the thickened plane that are repeated periodically in two directions. We first organize the components of a DP tangle into different it interlinked compounds, which are invariants of a DP tangle. The notion of interlinked compound leads to the classification of DP tangles according to their it 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.

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 that are repeated periodically in two directions. We first organize the components of a DP tangle into different it interlinked compounds, which are invariants of a DP tangle. The notion of interlinked compound leads to the classification of DP tangles according to their it 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 - tangles

KW - thickened torus

KW - motif

KW - topological invariant

KW - interlinked compound

KW - directional element

KW - directional type

KW - axis-motif

UR - https://www.mdpi.com/2073-8994/16/8/968

U2 - 10.48550/arXiv.2404.05092

DO - 10.48550/arXiv.2404.05092

M3 - Preprint

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BT - Directional Invariants of Doubly Periodic Tangles

PB - Cornell University - arXiv

ER -

Directional Invariants of Doubly Periodic Tangles

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Directional Invariants of Doubly Periodic Tangles

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