2005/03/17 by Miguel Bermúdez, M. Bermúdez, Bermúdez, M. +2
Arts and Humanities · Mathematics · Social Sciences · #22F10 #37C85 #Dynamical Systems (math.DS) #FOS: Mathematics #Linguistics and Discourse Analysis #Political and Social Issues #math.DS #msc:22F10 #msc:37C85
paper · pdf · doi:10.48550/arxiv.math/0503350
32 pages, 1 figure
openalex publication_date 2005/03/17 · arxiv created 2005/03/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the so-called BT-category of borelian-topological spaces: it will be a natural frame for a measurable classification of usual foliations and laminations. We focus on the two-dimensional case: borelian laminations by surfaces. We prove two main results: (1) Any borelian lamination by planes is the suspension of a \Z2-action on a Borel space iff this lamination is hyperfinite. (2) Any borelian lamination by surfaces is amenable if parabolic, i.e. if it admits a complex structure parabolic on each leaf. The third result is an improvement of (2) in case of laminations endowed with a transverse quasi-invariant measure μ. The statement is the following: (3) Any borelian lamination by planes, cylinders and tori is μ-amenable if and only if it admits a metric which is flat on μ-almost all leafs.