Teruaki Kitano

collaborators

6 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

Real analytic lift of foliations of Thurston and Tsuboi

Teruaki Kitano, Yoshihiko Mitsumatsu, Shigeyuki Morita

Thurston constructed codimension one foliations on $S^{3}$ thereby proved that the homomorphism $g v : I ¨ _{3} (B I^_{1}^{\infty}) \to R$ induced by the Godbillon-Vey i…

math.GT2026

A preorder on the set of links with applications to symmetric unions

Michel Boileau, Teruaki Kitano, Yuta Nozaki

For a link $L$ in the $3$ -sphere, the $I ¨ $ -orbifold group $G^{orb} (L)$ is defined as a quotient of the link group $G (L)$ of $L$ . When there exists an epimorphism $G^\mathrm{…

math.GT2026

An extended symmetric union with multiple tangle regions and its Alexander polynomial

Teruaki Kitano, Yasuharu Nakae

The authors recently introduced a new construction of a knot as an extended symmetric union of a knot with a single tangle region. In this paper, we generalize the construction to…

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…

math.GT2025

An extended symmetric union and its Alexander polynomial

Teruaki Kitano, Yasuharu Nakae

For prime knots $K_{1}$ and $K_{2}$ , we write $K_{1} \geq K_{2}$ if there is an epimorphism from the knot group of $K_{1}$ to that of $K_{2}$ which preserves the meridian. We construct a famil…