Groups and Embeddings in SL(2, ℂ)

Abstract

We give results on when a finitely generated torsion-free group does or does not embed in SL(2, ℂ). For instance, if we glue two copies of the figure 8 knot along its torus boundary, then the fundamental group of the resulting closed 3-manifold sometimes embeds in SL(2, ℂ) and sometimes does not, depending on the identification, whereas a graph of free groups with maximal cyclic edge groups need not embed, even if it is word hyperbolic.

Key Words:

• CSA group
• Graph of groups
• Limit group

2010 Mathematics Subject Classification:

• 20H20

Notes

Communicated by M. Dugald.