3 papers
math.GT2026
A ribbon knot which is not a symmetric union
Michel Boileau, Teruaki Kitano, Yuta Nozaki
A basic open question motivated by the study of ribbon knot diagrams asks whether every ribbon knot can be presented as a symmetric union. In this article, we give a negative answe…
math.GT2026
A preorder on the set of links with applications to symmetric unions
Michel Boileau, Teruaki Kitano, Yuta Nozaki
For a link in the -sphere, the -orbifold group is defined as a quotient of the link group of . When there exists an epimorphism $G^\mathrm{…
math.GT2025
On the genera of symmetric unions of knots
Michel Boileau, Teruaki Kitano, Yuta Nozaki
In the study of ribbon knots, Lamm introduced symmetric unions inspired by earlier work of Kinoshita and Terasaka. We show an identity between the twisted Alexander polynomials of…