Simple loop conjecture for limit groups
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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.
KeywordsFundamental Group Boundary Component Surface Group Limit Group Hyperbolic Group
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