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Israel Journal of Mathematics

, Volume 199, Issue 2, pp 527–545 | Cite as

Simple loop conjecture for limit groups

  • Larsen LouderEmail author
Article

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.

Keywords

Fundamental Group Boundary Component Surface Group Limit Group Hyperbolic Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Hebrew University Magnes Press 2014

Authors and Affiliations

  1. 1.Mathematical InstituteOxford UniversityOxfordUK

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