Details

Autor(en) / Beteiligte

• Austin, Tim

Titel

Integrable measure equivalence for groups of polynomial growth

Ist Teil von

• Groups, geometry and dynamics, 2016-01, Vol.10 (1), p.117-154

Ort / Verlag

Zuerich, Switzerland: European Mathematical Society Publishing House

Erscheinungsjahr

2016

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• Bader, Furman and Sauer have recently introduced the notion of integrable measure equivalence for nitely-generated groups. is is the sub-equivalence relation of measure equivalence obtained by insisting that the relevant cocycles satisfy an integrability condition. Th ey have used it to prove new classi cation results for hyperbolic groups. Th e present work shows that groups of polynomial growth are also quite rigid under integrable measure equivalence, in that if two such groups are equivalent then they must have bi-Lipschitz asymptotic cones. Th is will follow by proving that the cocycles arising from an integrable measure equivalence converge under re-scaling, albeit in a very weak sense, to bi-Lipschitz maps of asymptotic cones.