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On the commensurating full group
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abstract
We introduce a new Polish group, called the commensurating full group, associated to an ergodic measure-class preserving transformation of a standard atomless probability space. It is an analogue of the $\rm L^1$ full group defined by Le Ma\^itre, which does not need the transformation to preserve a measure to be defined. We prove, among others, that it is a complete invariant of flip conjugacy, and that it is quasi-isometric to the line in the sense of Rosendal.
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Cited by 1 Pith paper
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The analogue of Belinskaya's theorem for measure-preserving flows
Two free ergodic measure-preserving flows with isomorphic L¹ full groups are conjugate up to a constant time rescaling, which may reverse time.
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