Timeline for Homeomorphisms and "mod finite"
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Jul 5, 2020 at 11:25 | comment | added | Julien Melleray | @VilleSalo It's the "absorption theorem", theorem 12.1 in Putnam's book mentioned in my answer. It also follows from theorem 2.3 in Giordano--Putnam--Skau's paper in Crelle (which is, I think, the earliest proof). Indeed one can use the fact that both relations are induced by minimal homeomorphisms which have the same (unique) invariant measure, hence are orbit equivalent by Theorem 2.3 of Giordano--Putnam--Skau's Crelle article. | |
| Jul 4, 2020 at 20:46 | history | edited | LSpice | CC BY-SA 4.0 |
Link to book; name of paper
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| Jul 4, 2020 at 20:29 | comment | added | Ville Salo | @JulienMelleray: Pardon my orbit-equivalence ignorance, but what's the result you are referring to that implies there exists a homeomorphism $g$ such that $x =^* y \iff g(x) E g(y)$? | |
| Jul 4, 2020 at 19:17 | comment | added | Julien Melleray | Offhand, I do not know how to answer that one. The anwser might well be different! | |
| Jul 4, 2020 at 19:09 | comment | added | Bjørn Kjos-Hanssen | My follow-up question would be whether it helps if $E_0$ is preserved uniformly in the sense that whenever $x(n)$ and $y(n)$ agree above $n_0$ then there is an $m_0$ depending only on $n_0$ such that $f(x)(m)$ and $f(y)(m)$ agree above $m_0$... but that's for another day perhaps | |
| Jul 4, 2020 at 19:06 | comment | added | Julien Melleray | I'm not sure how needed they are to answer your question. They do play a key part in Giordano--Putnam--Skau's work, via a connection that Vershik made with topological dynamics. Equivalence relations induced by minimal homeomorphisms of the Cantor space are surprisingly complicated... | |
| Jul 4, 2020 at 19:03 | history | edited | Julien Melleray | CC BY-SA 4.0 |
typos...
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| Jul 4, 2020 at 19:02 | vote | accept | Bjørn Kjos-Hanssen | ||
| Jul 4, 2020 at 20:16 | |||||
| Jul 4, 2020 at 19:02 | comment | added | Bjørn Kjos-Hanssen | Surprised to see Bratteli diagrams make an appearance here... amazing! | |
| Jul 4, 2020 at 18:56 | history | answered | Julien Melleray | CC BY-SA 4.0 |