2 citations · 2 across the 9 of their papers we have counts for
9 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…
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…
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.…
Twisted Alexander invariants for the braid group associated with the Tong-Yang-Ma representation
Akihiro Takano
In this paper, we compute the twisted Alexander invariant of the braid group associated with the Tong-Yang-Ma representation.
The Long--Moody construction and twisted Alexander invariants
Akihiro Takano
In 1994, Long and Moody introduced a method to construct a new representation of the braid group from the representation of the braid group or the semidirect product of the braid g…
Extensions of Tong-Yang-Ma representation
Arthur Soulié, Akihiro Takano
In 1996, Tong, Yang and Ma defined a family of representations of the braid group which have the same dimensions as the (unreduced) Burau representations but are not equivalent. Th…