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arXiv · 2201.08213

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

Kenneth L. Baker·Dorothy Buck·Danielle O'Donnol·Allison H. Moore·Scott Taylor
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Abstract

We show that if a composite $\theta$-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 $\theta$-curve. We also prove similar results for 2-strand tangles and knotoids.

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Kenneth L. Baker, Dorothy Buck, Danielle O'Donnol, Allison H. Moore, Scott Taylor. 2022-01-20. Primality of theta-curves with proper rational tangle unknotting number one. https://arxiv.org/abs/2201.08213

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