Constructing thin subgroups commensurable with the figure-eight knot group

Constructing thin subgroups commensurable with the figure-eight knot group

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

The Figure Eight Knot Group is Conjugacy Separable

We prove that torsion free subgroups of PGL2(C) (abstractly) commensurable with the Euclidean Bianchi groups are conjugacy separable. As a consequence we deduce the result stated in the title.

The Symplectic Floer Homology of the Figure Eight Knot

In this paper, we compute the symplectic Floer homology of the figure eight knot. This provides first nontrivial knot with trivial symplectic Floer homology.

Congruence Subgroups of Groups Commensurable with PSL

The fundamental group of the double of the figure eight knot exterior is GFERF

We prove that the fundamental group of the double of the gure eight knot exterior admits a faithful discrete representation into SO(4; 1; R) for which the image group is separable on its geometrically nite subgroups. 2000 Mathematics Subject Classiication 20H10