4 papers
Types of Symmetries of Knots
Keegan Boyle, Nicholas Rouse, Ben Williams
We classify all finite group actions on knots in the 3-sphere. By geometrization, all such actions are conjugate to actions by isometries, and so we may use orthogonal representati…
Obstructions to free periodicity and symmetric L-space knots
Keegan Boyle, Nicholas Rouse, Ben Williams
We investigate a polynomial factorization problem that naturally arises from Hartley's factorization condition on the Alexander polynomial of freely periodic knots. We give a numbe…
Involutions on S^4
Keegan Boyle, Wenzhao Chen, Anthony Conway
This paper studies locally linear involutions on S^4. Our main theorem shows that any such involution with a 1-dimensional fixed-point set is necessarily linear, provided the fixed…
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…