16 citations · 63 across the 30 of their papers we have counts for
32 papers
Dehn filling and the knot group II: Ubiquity of persistent elements
Tetsuya Ito, Kimihiko Motegi, Masakazu Teragaito
Let be a nontrivial knot in . We say that an element of the knot group is \textit{persistent} if it remains nontrivial under all nontrivial Dehn fillings. Such elem…
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 --manifold obtained by non-trivial Dehn surgery on a non-trivial knot is never simply c…
Asymptotic behavior of unknotting numbers of links in a twist family
Kenneth L. Baker, Yasuyuki Miyazawa, Kimihiko Motegi
By twisting a given link along an unknotted circle , we obtain an infinite family of links . We introduce the ``stable unknotting number'' which describes the asy…
Every non-trivial knot group is fully residually perfect
Tetsuya Ito, Kimihiko Motegi, Masakazu Teragaito
Given a class of groups we say that a group is fully residually if for any finite subset of , there exists an epimorphism from to a group…
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…
Classification of generalized torsion elements of order two in 3-manifold groups
Keisuke Himeno, Kimihiko Motegi, Masakazu Teragaito
Let be a group and a non-trivial element in . If some non-empty finite product of conjugates of equals to the identity, then is called a generalized torsion elem…