Limit groups, positive-genus towers and measure equivalence

Abstract

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.

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

References in corpus (1)

• Limit groups as limits of free groups: compactifying the set of free groups

Cited by in corpus (1)

• Elementarily free groups are subgroup separable