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Limit groups, positive-genus towers and measure equivalence

Martin R Bridson·Michael Tweedale·Henry Wilton
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Abstract

By definition, an $ω$-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 $ω$-residually free tower. By combining this with results of Gaboriau, we prove that elementarily free groups are measure equivalent to free groups.

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Martin R Bridson, Michael Tweedale, Henry Wilton. 2006-11-07. Limit groups, positive-genus towers and measure equivalence. https://arxiv.org/abs/math/0511275

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