Primality of theta-curves with proper rational tangle unknotting number one
Kenneth L. Baker, Dorothy Buck, Danielle O'Donnol, Allison H. Moore,, Scott Taylor
TL;DR
This paper characterizes composite theta-curves with proper rational unknotting number one, showing they decompose into simpler components, and extends results to 2-strand tangles and knotoids.
Contribution
It provides a structural classification of certain theta-curves with unknotting number one and generalizes the results to tangles and knotoids.
Findings
Composite theta-curves with unknotting number one are decomposable into an order 2 sum of a knot and a trivial theta-curve.
Similar decomposition results hold for 2-strand tangles.
The paper extends these structural results to knotoids.
Abstract
We show that if a composite -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 -curve. We also prove similar results for 2-strand tangles and knotoids.
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Geometric and Algebraic Topology · Algebraic Geometry and Number Theory