Primality of theta-curves with proper rational tangle unknotting number one

preprint2022arXivOpen access

We show that if a composite $θ$ -curve has (proper rational) unknotting number one, then it is the order 2 sum of a (proper rational) unknotting number one knot and a trivial $θ$ -curve. We also prove similar results for 2-strand tangles and knotoids.

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Primality of theta-curves with proper rational tangle unknotting number one

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