Lupini, Martino and Panagiotopoulos, Aristotelis (2018) Games orbits play and obstructions to Borel reducibility. Groups, Geometry, and Dynamics, 12 (4). pp. 1461-1483. ISSN 1661-7207. doi:10.4171/GGD/475. https://resolver.caltech.edu/CaltechAUTHORS:20180410-144608293
![[img]](https://authors.library.caltech.edu/style/images/fileicons/application_pdf.png) |
PDF
- Submitted Version
See Usage Policy. 255kB |
Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20180410-144608293
Abstract
We introduce a new, game-theoretic approach to anti-classification results for orbit equivalence relations. Within this framework, we give a short conceptual proof of Hjorth’s turbulence theorem. We also introduce a new dynamical criterion providing an obstruction to classification by orbits of CLI groups. We apply this criterion to the relation of equality of countable sets of reals, and the relations of unitary conjugacy of unitary and selfadjoint operators on the separable infinite-dimensional Hilbert space.
| Item Type: | Article | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Related URLs: |
| |||||||||
| ORCID: |
| |||||||||
| Additional Information: | © 2018 European Mathematical Society. Received February 4, 2017. Published online: 2018-11-01. This work was initiated during a visit of Aristotelis Panagiotopoulos at the California Institute of Technology in the Spring 2016. The authors gratefully acknowledge the hospitality and the financial support of the Institute. M. Lupini was partially supported by the NSF Grant DMS-1600186. | |||||||||
| Funders: |
| |||||||||
| Subject Keywords: | Polish group, Polish groupoid, turbulence, orbit equivalence relation, Borel game, CLI group, non-Archimedean group | |||||||||
| Issue or Number: | 4 | |||||||||
| Classification Code: | 2000 Mathematics Subject Classification. Primary 03E15, 54H20; Secondary 20L05, 54H05 | |||||||||
| DOI: | 10.4171/GGD/475 | |||||||||
| Record Number: | CaltechAUTHORS:20180410-144608293 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20180410-144608293 | |||||||||
| Official Citation: | Lupini Martino, Panagiotopoulos Aristotelis: Games orbits play and obstructions to Borel reducibility. Groups Geom. Dyn. 12 (2018), 1461-1483. doi: 10.4171/GGD/475 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 85733 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 11 Apr 2018 18:40 | |||||||||
| Last Modified: | 15 Nov 2021 20:31 |
Repository Staff Only: item control page
