Directional Invariants of Doubly Periodic Tangles

Ioannis Diamantis; Sofia Lambropoulou; Sonia Mahmoudi

doi:10.3390/sym16080968

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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 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 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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Ioannis Diamantis, Sofia Lambropoulou, Sonia Mahmoudi. 2024-04-07. Directional Invariants of Doubly Periodic Tangles. https://doi.org/10.3390/sym16080968

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