Tetsuya Ito

collaborators

3 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

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…