Linking numbers for periodic tangles

Yuka Kotorii; Ken'ichi Yoshida

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arXiv · 2509.24568

Linking numbers for periodic tangles

Yuka Kotorii·Ken'ichi Yoshida

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Abstract

Periodic tangles are 1-dimensional submanifolds in the 3-space with translational symmetry. In this paper, we define the linking numbers for singly, doubly, and triply periodic tangles using appropriate motifs and show that they are well-defined and invariant under link-homotopy. Furthermore, we extend the notion to the higher order linking numbers for singly periodic tangles.

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Yuka Kotorii, Ken'ichi Yoshida. 2025-09-29. Linking numbers for periodic tangles. https://arxiv.org/abs/2509.24568

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