Limit groups, positive-genus towers and measure equivalence

Bridson, Martin R; Tweedale, Michael; Wilton, Henry

Limit groups, positive-genus towers and measure equivalence

Authors

Bridson, Martin R

Tweedale, Michael

Wilton, Henry

Description

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