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This paper investigates the relationship between conjugacy classes of Thompson's group F and the construction of unoriented links.

June 12, 2026

On Thompson Knot Theory and Conjugacy Classes of Thompson's Group f

Key Points

This paper investigates the relationship between conjugacy classes of Thompson's group F and the construction of unoriented links.
Analyzed the method introduced by Jones for constructing unoriented links from elements of Thompson's group F.
Identified sequences of elements from distinct conjugacy classes that yield specific unoriented links.
Constructed 2-bridge links from elements within the conjugacy classes of x 0 and x 1.
Successfully demonstrated the creation of unoriented links from elements of distinct conjugacy classes in F.
Showed that specific sequences can construct a variety of 2-bridge links from chosen conjugacy classes.

Abstract

Jones introduced a method to construct unoriented links from elements of the Thompson’s group F, and proved that any link can be obtained by this construction. In this paper, we study the relation between conjugacy classes of the group F and the links being constructed. For each unoriented link L, we find a sequence of elements of F from distinct conjugacy classes which yield L via Jones’ construction. We also show that a sequence of 2-bridge links can be constructed from elements in the conjugacy class of x 0 (resp. x 1 ).

On Thompson Knot Theory and Conjugacy Classes of Thompson's Group f

Key Points

Abstract

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