Superrigidity and countable Borel equivalence relations

✍ Scribed by Simon Thomas

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 254 KB
• Volume: 120
• Category: Article
• ISSN: 0168-0072
• DOI: 10.1016/s0168-0072(02)00068-4

✦ Synopsis

We formulate a Borel version of a corollary of Furman's superrigidity theorem for orbit equivalence and present a number of applications to the theory of countable Borel equivalence relations. In particular, we prove that the orbit equivalence relations arising from the natural actions of SL3(Z) on the projective planes over the various p-adic ÿelds are pairwise incomparable with respect to Borel reducibility.