Limit groups, positivegenus towers and measure equivalence
Abstract
By definition, an $\omega$residually free tower is positivegenus if all surfaces used in its construction are of positive genus. We prove that every limit group is virtually a subgroup of a positivegenus $\omega$residually free tower. By combining this with results of Gaboriau, we prove that elementarily free groups are measure equivalent to free groups.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 November 2005
 arXiv:
 arXiv:math/0511275
 Bibcode:
 2005math.....11275B
 Keywords:

 Mathematics  Group Theory;
 Mathematics  Dynamical Systems;
 20F65;
 37A20 (20E05;
 22F10)
 EPrint:
 10 pages