Limit groups, positive-genus towers and measure-equivalence

• Autores: Martin R. Bridson, Michael Tweedale, Henry Wilton
• Localización: Ergodic theory and dynamical systems, ISSN 0143-3857, Vol. 27, Nº 3, 2007, págs. 703-712
• Idioma: inglés
• DOI: 10.1017/s0143385706001039
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• Resumen

  • 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.