Limit groups, positive-genus towers and measure-equivalence
نویسندگان
چکیده
منابع مشابه
Limit Groups, Positive-genus Towers and Measure Equivalence
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 construction with results of Gaboriau, we prove that elementarily free groups are measure equivalent to free groups.
متن کاملN ov 2 00 5 Limit groups , positive - genus towers and measure equivalence
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. Measure equivalence was introduced by M. Gromov in [8] as a measu...
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We introduce the k-peg Hanoi automorphisms and Hanoi self-similar groups, a generalization of the Hanoi Towers groups, and give conditions for them to be contractive. We analyze the limit spaces of a particular family of contracting Hanoi groups, H (k) c , and show that these are the unique maximal contracting Hanoi groups under a suitable symmetry condition. Finally, we provide partial results...
متن کاملar X iv : m at h / 05 11 27 5 v 2 [ m at h . G R ] 7 N ov 2 00 6 LIMIT GROUPS , POSITIVE - GENUS TOWERS AND MEASURE EQUIVALENCE
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 construction with results of Gaboriau, we prove that elementarily free groups are measure equivalent to free groups.
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We show that the L-torsion of finite aspherical CW-complexes with boundedly measure equivalent fundamental groups agrees up to a factor given by the index of the measure equivalence.
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2007
ISSN: 0143-3857,1469-4417
DOI: 10.1017/s0143385706001039