Constructing thin subgroups commensurable with the figure-eight knot group

TL;DR

This paper constructs infinitely many lattices in SL(4,R) that contain thin subgroups related to the figure-eight knot group, expanding understanding of their algebraic and geometric properties.

Contribution

It introduces a method to find infinitely many lattices with thin subgroups commensurable with the figure-eight knot group in SL(4,R).

Findings

Existence of infinitely many such lattices.

Construction of thin subgroups within these lattices.

Relationship established between lattices and the figure-eight knot group.

Abstract

In this paper we find infinitely many lattices in $SL(4,\mathbb{R})$ each of which contains thin subgroups commensurable with the figure-eight knot group.