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math.GT2024
Equivariant unknotting numbers of strongly invertible knots
Keegan Boyle, Wenzhao Chen
We study symmetric crossing change operations for strongly invertible knots. Our main theorem is that the most natural notion of equivariant unknotting number is not additive under…
math.GT2024
Freely 2-periodic knots have two canonical components
Keegan Boyle, Nicholas Rouse
We prove that the SL(2, C) character variety of a hyperbolic, freely 2-periodic knot has two canonical components. We also prove that the hyperbolic torsion polynomial of such a kn…