Limit groups, positive-genus towers and measure equivalence

Mathematics – Group Theory

Scientific paper

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10 pages; no figures. Minor changes; now to appear in Ergod. Th. & Dynam. Sys

Scientific paper

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 with results of Gaboriau, we prove that
elementarily free groups are measure equivalent to free groups.

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