Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

The action of $SL(2,\mathbb{Z} )$ on the subsets of $\mathbb{Z} ^2$


Author: Su Gao
Journal: Proc. Amer. Math. Soc. 129 (2001), 1507-1512
MSC (2000): Primary 03E15, 15A36; Secondary 20A10, 20E05
DOI: https://doi.org/10.1090/S0002-9939-00-05721-X
Published electronically: October 25, 2000
MathSciNet review: 1814177
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that the orbit equivalence relation of the canonical action of $SL(2,\mathbb{Z} )$ on the subsets of $\mathbb{Z} ^2$ is a universal countable Borel equivalence relation.


References [Enhancements On Off] (What's this?)

  • [DJK] R. DOUGHERTY, S. JACKSON AND A. S. KECHRIS, The structure of hyperfinite Borel equivalence relations, Trans. Amer. Math. Soc. 341 (1994), 193-225. MR 94c:03066
  • [Hj] G. HJORTH, Around nonclassifiability for countable torsion free abelian groups, preprint, 1998.
  • [HK] G. HJORTH AND A. S. KECHRIS, Borel equivalence relations and classification of countable models, Ann. Pure Appl. Logic 82 (1996), 221-272. MR 99m:03073
  • [JKL] S. JACKSON, A. S. KECHRIS AND A. LOUVEAU, Countable Borel equivalence relations, manuscript.
  • [Ke1] A. S. KECHRIS, Countable sections for locally compact group actions. II, Proc. Amer. Math. Soc. 120 (1994), 241-247. MR 94b:22004
  • [Ke2] A. S. KECHRIS, On the classification problem for rank $2$ torsion-free abelian groups, preprint, 1999.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 03E15, 15A36, 20A10, 20E05

Retrieve articles in all journals with MSC (2000): 03E15, 15A36, 20A10, 20E05


Additional Information

Su Gao
Affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
Email: sugao@its.caltech.edu

DOI: https://doi.org/10.1090/S0002-9939-00-05721-X
Keywords: Borel reducibility, universal countable Borel equivalence relation, free group, free action
Received by editor(s): June 21, 1999
Received by editor(s) in revised form: August 30, 1999
Published electronically: October 25, 2000
Communicated by: Carl G. Jockusch, Jr.
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society