Resumen de Limit groups, positive-genus towers and measure-equivalence

Martin R. Bridson, Michael Tweedale, Henry Wilton

• 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.