This paper defines linking numbers for periodic tangles, suggesting they remain invariant under link-homotopy.
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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Kotorii et al. (2025) studied this question.
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