Primality of theta-curves with proper rational tangle unknotting number one
We show that if a composite <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="theta"> <mml:semantics> <mml:mi>θ</mml:mi> <mml:annotation encoding="application/x-tex">\theta</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-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 <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="theta"> <mml:semantics> <mml:mi>θ</mml:mi> <mml:annotation encoding="application/x-tex">\theta</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-curve. We also prove similar results for 2-strand tangles and knotoids.
Authors
- Dorothy Buck (ORCID: https://orcid.org/0000-0002-3662-6465)
- Allison H. Moore (ORCID: https://orcid.org/0000-0002-3266-9601)
- Kenneth L. Baker (ORCID: https://orcid.org/0000-0001-9410-0106)
- Danielle O’Donnol
- Scott Douglas Taylor (ORCID: https://orcid.org/0000-0001-5449-5940)
Institutions
- University of Miami (US)
- Duke University (US)
- Virginia Commonwealth University (US)
- Colby College (US)
Publication Details
- Journal
- Transactions of the American Mathematical Society Series B
- Published
- 2025-03-04
- DOI
- https://doi.org/10.1090/btran/217
- Primary Topic
- Advanced Numerical Analysis Techniques
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Science Foundation
- Simons Foundation
- Thomas F. and Kate Miller Jeffress Memorial Trust
- National Youth Science Foundation
- Leverhulme Trust