Groups and Embeddings in SL(2, ℂ)

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.This is the author accepted manuscript. The final version is available from Taylor & Francis via http://dx.doi.org/10.1080/00927872.2014.97534