Simple loop conjecture for limit groups

Abstract

There are noninjective maps from surface groups to limit groups that don't kill any simple closed curves. As a corollary, there are noninjective all-loxodromic representations of surface groups to SL(2,C) that don't kill any simple closed curves, answering a question of Minsky. There are also examples, for any k, of noninjective all-loxodromic representations of surface groups killing no curves with self intersection number at most k.

13 pages, 2 figures, to appear in Israel Journal of Mathematics (accepted on Nov 5 2012)

Cited by in corpus (2)

• Non-faithful representations of surface groups into SL(2,C) which kill no simple closed curve
• Groups possessing only indiscrete embeddings in SL(2,C)