The absorption theorem for affable equivalence relations
| dc.creator | Giordano, Thierry | |
| dc.creator | Matui, Hiroki | |
| dc.creator | Putnam, Ian F. | |
| dc.creator | Skau, Christian F. | |
| dc.date | 2007-05-23 | |
| dc.date | 2007-10-09 | |
| dc.date.accessioned | 2026-07-07T08:34:32Z | |
| dc.date.available | 2026-07-07T08:34:32Z | |
| dc.description | We prove a result about extension of a minimal AF-equivalence relation R on the Cantor set X, the extension being `small' in the sense that we modify R on a thin closed subset Y of X. We show that the resulting extended equivalence relation S is orbit equivalent to the original R, and so, in particular, S is affable. Even in the simplest case--when Y is a finite set--this result is highly non-trivial. The result itself--called the absorption theorem--is a powerful and crucial tool for the study of the orbit structure of minimal Z^n-actions on the Cantor set [GMPS]. The absorption theorem is a significant generalization of the main theorem proved in [GPS2]. However, we shall need a few key results from [GPS2] in order to prove the absorption theorem. | |
| dc.identifier | https://arxiv.org/abs/0705.3270 | |
| dc.identifier | http://arxiv.org/abs/0705.3270 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/139470 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Operator Algebras | |
| dc.subject | 37B05 | |
| dc.title | The absorption theorem for affable equivalence relations | |
| dc.type | text |