6 citations · 13 across the 15 of their papers we have counts for
17 papers
Myopic Tutte polynomials and Khovanov homology in
Keegan Boyle, Dean Spyropoulos
We present a "myopic" Tutte polynomial for graphs on which takes only nullhomologous spanning subgraphs as input. It recovers the generalized Krushkal polynomial an…
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…
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…
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…
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…
Equivariant topological slice disks and negative amphichiral knots
Keegan Boyle, Wenzhao Chen
We show that any strongly negative amphichiral knot with a trivial Alexander polynomial is equivariantly topologically slice.
Negative amphichiral knots and the half-Conway polynomial
Keegan Boyle, Wenzhao Chen
In 1979, Hartley and Kawauchi proved that the Conway polynomial of a strongly negative amphichiral knot factors as . In this paper, we normalize the factor to def…
Equivariant cobordisms between freely-periodic knots
Keegan Boyle, Jeffrey Musyt
We consider free symmetries on cobordisms between knots. We classify which freely periodic knots bound equivariant surfaces in the 4-ball in terms of corresponding homology classes…
Strongly invertible knots, invariant surfaces, and the Atiyah-Singer signature theorem
Antonio Alfieri, Keegan Boyle
We use the G-signature theorem to define an invariant of strongly invertible knots analogous to the knot signature.
Equivariantly slicing strongly negative amphichiral knots
Keegan Boyle, Ahmad Issa
We prove obstructions to a strongly negative amphichiral knot bounding an equivariant slice disk in the 4-ball using the determinant, Spinc-structures and Donaldson's theorem. Of t…
Equivariant 4-genera of strongly invertible and periodic knots
Keegan Boyle, Ahmad Issa
We study the equivariant genera of strongly invertible and periodic knots. Our techniques include some new strongly invertible concordance group invariants, Donaldson's theorem, an…
Involutions of alternating links
Keegan Boyle
Let be an alternating prime non-split link in . We use the category of flypes between reduced alternating diagrams for to classify involutions on . As consequences,…
Odd Order Group Actions on Alternating Knots
Keegan Boyle
Let K be a an alternating prime knot in the 3-sphere. We investigate the category of flypes between reduced alternating diagrams for K. As a consequence, we show that any odd prime…
Quotients of Definite Periodic Knots are Definite
Keegan Boyle
A knot is definite if . We prove that the quotient of a definite periodic knot is definite by considering equivariant minimal genus Seifert surfaces.
Rank Inequalities on Knot Floer Homology of Periodic Knots
Keegan Boyle
Let be a 2-periodic knot in with quotient . We prove a rank inequality between the knot Floer homology of and the knot Floer homology of $K…
On The Virtual Cosmetic Surgery Conjecture
Keegan Boyle
Let K be a knot in S^3, and M and M' be distinct Dehn surgeries along K. We investigate when M covers M'. When K is a torus knot, we provide a complete classification of such cover…