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Jan. 2006 Classification of the mapping class groups up to measure equivalence
Yoshikata Kida
Proc. Japan Acad. Ser. A Math. Sci. 82(1): 4-7 (Jan. 2006). DOI: 10.3792/pjaa.82.4


We study the mapping class groups of compact orientable surfaces from the viewpoint of measure equivalence. In this paper, we announce some classification result of the mapping class groups in terms of measure equivalence and the result that there exist various kinds of discrete groups which are not measure equivalent to the mapping class groups. As a byproduct of the proof, it turns out that the mapping class group is exact.


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Yoshikata Kida. "Classification of the mapping class groups up to measure equivalence." Proc. Japan Acad. Ser. A Math. Sci. 82 (1) 4 - 7, Jan. 2006.


Published: Jan. 2006
First available in Project Euclid: 1 February 2006

zbMATH: 1130.37309
MathSciNet: MR2198438
Digital Object Identifier: 10.3792/pjaa.82.4

Primary: 20F38 , 37A20

Keywords: measure equivalence , orbit equivalence , the curve complex , The mapping class group

Rights: Copyright © 2006 The Japan Academy


Vol.82 • No. 1 • Jan. 2006
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