2 citations · 6 across the 10 of their papers we have counts for
11 papers
Presentations of the cactus Thompson group
Yuya Kodama, Akihiro Takano
We give infinite and finite presentations of the cactus Thompson group. This group was introduced as by Witzel and Zaremsky, who combined Thompson's group with…
Distorted and undistorted subgroups of the Lodha-Moore group
Yuya Kodama
We show that the Baumslag-Solitar group is undistorted in the Lodha-Moore group using an explicit lower bound for the word length of . We also show that Thomps…
Metrics for quandles
Kohei Iwamoto, Ryoya Kai, Yuya Kodama
A quandle is an algebraic system originating in knot theory, which can be regarded as a generalization of the conjugation of groups. This structure naturally defines two subgroups…
The Lodha--Moore groups and their -adic generalizations are not SCY
Yuya Kodama, Akihiro Takano
A closed 4-manifold is symplectic Calabi--Yau (SCY) if its canonical class is trivial. Friedl and Vidussi proved that Thompson's group cannot be the fundamental group of any SC…
Divergence functions of higher-dimensional Thompson's groups
Yuya Kodama
We prove that higher-dimensional Thompson's groups have linear divergence functions. By the work of Druţu, Mozes, and Sapir, this implies none of the asymptotic cones of has a…
Alexander's theorem for stabilizer subgroups of Thompson's group
Yuya Kodama, Akihiro Takano
In 2017, Jones studied the unitary representations of Thompson's group and defined a method to construct knots and links from . One of his results is that any knot or link c…
The -colorable subgroup of Thompson's group
Yuya Kodama, Akihiro Takano
Recently, Jones introduced a method of constructing knots and links from elements of Thompson's group by using its unitary representations. He also defined several subgroups of…
The -colorable subgroup of Thompson's group and tricolorability of links
Yuya Kodama, Akihiro Takano
Starting from the work by Jones on representations of Thompson's group , subgroups of with interesting properties have been defined and studied. One of these subgroups is ca…
Virtual Thompson's group
Yuya Kodama, Akihiro Takano
For virtual knot theory, the virtual braid group was defined by generalizing the braid group. It was proved that any virtual link can be obtained by the closure of a virtual braid.…
An -adic generalization of the Lodha-Moore group
Yuya Kodama
We generalized the Lodha-Moore group into -adic and showed analogues in the Lodha-Moore group of properties between the Thompson group and the generalized Thompson group $F(…
Divergence function of the braided Thompson group
Yuya Kodama
We prove that the braided Thompson group has a linear divergence function. By the work of Druţu, Mozes, and Sapir, this leads none of asymptotic cones of has a cut-point.