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 D… Show more
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