Kimihiko Motegi

activity

20242026

collaborators

7 papers

math.GT2026

Dehn filling and the knot group II: Ubiquity of persistent elements

Tetsuya Ito, Kimihiko Motegi, Masakazu Teragaito

Let $K$ be a nontrivial knot in $S^{3}$ . We say that an element of the knot group $G (K)$ is \textit{persistent} if it remains nontrivial under all nontrivial Dehn fillings. Such elem…

math.GT2026

Group theoretic perspective on Dehn fillings: Property P conjecture and beyond

Tetsuya Ito, Kimihiko Motegi, Masakazu Teragaito

The Property P Conjecture, which was settled by Kronheimer and Mrowka, asserts that every $3$ --manifold obtained by non-trivial Dehn surgery on a non-trivial knot is never simply c…

math.GT2025

Knots not detected by any trace

Kenneth L. Baker, Marc Kegel, Kimihiko Motegi

The first and last named authors have demonstrated the existence of knots for which every integral slope is non-characterizing. In this short note, we extend this result in two way…

math.GT2025

Dehn filling and the knot group I: Realization Property

Tetsuya Ito, Kimihiko Motegi, Masakazu Teragaito

Each $r$ -Dehn filling of the exterior $E (K)$ of a knot $K$ in $S^{3}$ produces a $3$ -manifold $K (r)$ , and induces an epimorphism from the knot group $G (K) = I ¨ _{1} (E (K))$ to $Ï_1(K(r)…

math.GT2025

Every non-trivial knot group is fully residually perfect

Tetsuya Ito, Kimihiko Motegi, Masakazu Teragaito

Given a class $P$ of groups we say that a group $G$ is fully residually $P$ if for any finite subset $F$ of $G$ , there exists an epimorphism from $G$ to a group…

math.GT2025

Asymptotic behavior of unknotting numbers of links in a twist family

Kenneth L. Baker, Yasuyuki Miyazawa, Kimihiko Motegi

By twisting a given link $L$ along an unknotted circle $c$ , we obtain an infinite family of links ${L_{n}}$ . We introduce the ``stable unknotting number'' which describes the asy…