Limit groups, positive-genus towers and measure-equivalence

@article{Bridson2005LimitGP,
  title={Limit groups, positive-genus towers and measure-equivalence},
  author={Martin R. Bridson and Michael Tweedale and Henry Wilton},
  journal={Ergodic Theory and Dynamical Systems},
  year={2005},
  volume={27},
  pages={703 - 712}
}
By definition, an $\omega$-residually free tower is positive-genus if all surfaces used in its construction are of positive-genus. We prove that every limit group is virtually a subgroup of a positive-genus, $\omega$-residually free tower. By combining this construction with results of Gaboriau, we prove that elementarily free groups are measure-equivalent to free groups. 

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