Abstract
Recently, Jones introduced a method of constructing knots and links from elements of Thompson’s group F by using its unitary representations. He also de ned a subgroup of F as the stabilizer subgroup, called the 3-colorable subgroup. We proved that all knots and links obtained from non-trivial elements of this group are 3-colorable. In this talk, we extend this result to any odd integer p greater than two. Namely, we de ne the p-colorable subgroup of F whose non-trivial elements yield p-colorable knots and links, and show that it is isomorphic to the Brown{Thompson group. This is joint work with Yuya Kodama (Tokyo Metropolitan University).
Content
The Gist
We will define the 3-colorable subgroup. We will show the corresponding knots are exactly the 3-colorable group.
We explain how the elements of Thompsons group can be understood as a set of homeomorphisms or as trees. We can switch from the tree to the homeomorphism by looking at how the tree partitions the space.
We did some things
We did some things
Generalized Thompsons group
We looked at brown-thompson groups