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.

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Correspondence to Larsen Louder.

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Louder, L. Simple loop conjecture for limit groups. Isr. J. Math. 199, 527–545 (2014). https://doi.org/10.1007/s11856-013-0051-6

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Keywords

  • Fundamental Group
  • Boundary Component
  • Surface Group
  • Limit Group
  • Hyperbolic Group