Publishing type：Research paper (scientific journal)   Publisher：Mathematical Society of Japan (Project Euclid)  

DOI： 10.2969/jmsj/91339133

Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

DOI： 10.1016/j.jalgebra.2023.07.014

Publishing type：Research paper (scientific journal)   Publisher：Taylor & Francis  

DOI： 10.1080/00927872.2023.2223716

Publishing type：Research paper (scientific journal)   Publisher：Duke University Press  

DOI： 10.1215/21562261-10428532

We prove that higher-dimensional Thompson's groups have linear divergence
functions. By the work of Dru\c{t}u, Mozes, and Sapir, this implies none of the
asymptotic cones of $nV$ has a cut-point.

arXiv

Other Link： http://arxiv.org/pdf/2405.19923v1

In 2017, Jones studied the unitary representations of Thompson's group $F$
and defined a method to construct knots and links from $F$. One of his results
is that any knot or link can be obtained from an element of this group, which
is called Alexander's theorem. On the other hand, Thompson's group $F$ has many
subgroups and it is known that there exist various subgroups which satisfy or
do not satisfy Alexander's theorem. In this paper, we prove that almost all
stabilizer subgroups under the natural action on the unit interval satisfy
Alexander's theorem.

arXiv

Other Link： http://arxiv.org/pdf/2306.13398v1

Recently, Jones introduced a method of constructing knots and links from
elements of Thompson's group $F$ by using its unitary representations. He also
defined several subgroups of $F$ as the stabilizer subgroups and some
researchers studied them algebraically. One of the subgroups is called the
3-colorable subgroup $\mathcal{F}$, and the authors proved that all knots and
links obtained from non-trivial elements of $\mathcal{F}$ are 3-colorable. In
this paper, for any odd integer $p$ greater than two, we define the
$p$-colorable subgroup of $F$ whose non-trivial elements yield $p$-colorable
knots and links and show it is isomorphic to the certain Brown--Thompson group.

arXiv

Other Link： http://arxiv.org/pdf/2302.10060v1