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Games orbits play and obstructions to Borel reducibility

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. https://resolver.caltech.edu/CaltechAUTHORS:20180410-144608293

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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:
URLURL TypeDescription
https://doi.org/10.4171/GGD/475DOIArticle
https://arxiv.org/abs/1612.08284arXivDiscussion Paper
ORCID:
AuthorORCID
Lupini, Martino0000-0003-1588-7057
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:
Funding AgencyGrant Number
CaltechUNSPECIFIED
NSFDMS-1600186
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
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:03 Oct 2019 19:34

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