Limit groups, positive-genus towers and measure equivalence

MR Bridson; MP Tweedale; H Wilton

doi:10.1017/S0143385706001039

Limit groups, positive-genus towers and measure equivalence

MR Bridson, MP Tweedale, H Wilton

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

8 Citations (Scopus)

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 construction with results of Gaboriau, we prove that elementarily free groups are measure-equivalent to free groups.

Translated title of the contribution	Limit groups, positive-genus towers and measure equivalence
Original language	English
Pages (from-to)	703 - 712
Number of pages	10
Journal	Ergodic Theory and Dynamical Systems
Volume	27 (3)
DOIs	https://doi.org/10.1017/S0143385706001039
Publication status	Published - Jun 2007

Bibliographical note

Publisher: Cambridge University Press
Other identifier: EISSN 1469-4417

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10.1017/S0143385706001039

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title = "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 construction with results of Gaboriau, we prove that elementarily free groups are measure-equivalent to free groups.",

author = "MR Bridson and MP Tweedale and H Wilton",

note = "Publisher: Cambridge University Press Other identifier: EISSN 1469-4417",

year = "2007",

month = jun,

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T1 - Limit groups, positive-genus towers and measure equivalence

AU - Bridson, MR

AU - Tweedale, MP

AU - Wilton, H

N1 - Publisher: Cambridge University Press Other identifier: EISSN 1469-4417

PY - 2007/6

Y1 - 2007/6

N2 - 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.

AB - 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.

U2 - 10.1017/S0143385706001039

DO - 10.1017/S0143385706001039

M3 - Article (Academic Journal)

SN - 1469-4417

VL - 27 (3)

SP - 703

EP - 712

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

ER -

Limit groups, positive-genus towers and measure equivalence

Abstract

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