Non-faithful representations of surface groups into SL(2,C) which kill no simple closed curve

Abstract

We give counterexamples to a version of the simple loop conjecture in which the target group is PSL(2,C). These examples answer a question of Minsky in the negative.

23 pages, 3 figures. Version 3 incorporates additional referee comments, especially improving the appendix

References in corpus (3)

• Short geodesics and end invariants
• Simple loop conjecture for limit groups
• Groups possessing only indiscrete embeddings in SL(2,C)

Cited by in corpus (3)

• Topology of character varieties of Abelian groups
• Homotopy Groups of Free Group Character Varieties
• Surface group representations in ${\mathrm{SL}}_2(\mathbb{C})$ with finite mapping class orbits