Abstract
Starting from the work by Jones on representations of Thompson's group F, subgroups of F with interesting properties have been defined and studied. One of these subgroups is called the 3-colorable subgroup F, which consists of elements whose “regions” given by their tree diagrams are 3-colorable. On the other hand, in his work on representations, Jones also gave a method to construct knots and links from elements of F. Therefore it is a natural question to explore a relationship between elements in F and 3-colorable links in the sense of knot theory. In this paper, we show that all elements in F give 3-colorable links.
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