Geodesic
Games orbits play and obstructions to Borel reducibility
Martino Lupini1 orcid ; Aristotelis Panagiotopoulos2
1California Institute of Technology, Pasadena, USA
2California Institute of Technology, Pasadena, USA and University of Illinois, Urbana, USA
Groups, geometry, and dynamics, Tome 12 (2018) no. 4, pp. 1461-1483

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DOI

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.
DOI : 10.4171/ggd/475
Classification : 54-XX, 03-XX, 20-XX
Mots-clés : Polish group, Polish groupoid, turbulence, orbit equivalence relation, Borel game, CLI group, non-Archimedean group

Martino Lupini  1   ; Aristotelis Panagiotopoulos  2

1 California Institute of Technology, Pasadena, USA
2 California Institute of Technology, Pasadena, USA and University of Illinois, Urbana, USA 
Martino Lupini; Aristotelis Panagiotopoulos. Games orbits play and obstructions to Borel reducibility. Groups, geometry, and dynamics, Tome 12 (2018) no. 4, pp. 1461-1483. doi: 10.4171/ggd/475
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     title = {Games orbits play and obstructions to {Borel} reducibility},
     journal = {Groups, geometry, and dynamics},
     pages = {1461--1483},
     year = {2018},
     volume = {12},
     number = {4},
     doi = {10.4171/ggd/475},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/475/}
}
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