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Limit groups, positive-genus towers and measure-equivalence

Published online by Cambridge University Press:  12 February 2007

MARTIN R. BRIDSON,
MICHAEL TWEEDALE and
HENRY WILTON
MARTIN R. BRIDSON
Affiliation:
Department of Mathematics, Imperial College, London SW7 2AZ, UK (e-mail: m.bridson@imperial.ac.uk)
MICHAEL TWEEDALE
Affiliation:
Department of Mathematics, University of Bristol, Bristol BS8 1TW, UK (e-mail: m.tweedale@bristol.ac.uk)
HENRY WILTON
Affiliation:
Department of Mathematics, 1 University Station C1200, Austin, TX 78712, USA (e-mail: henry.wilton@math.utexas.edu)
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Abstract

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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.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 27 , Issue 3 , June 2007, pp. 703 - 712
Copyright
2007 Cambridge University Press