The Mapping Class Group from the Viewpoint of Measure Equivalence Theory
Author： Yoshikata Kida
Publisher： American Mathematical Society
Publication year： 2013
E-ISBN: 9781470405229
P-ISBN(Paperback): 9780821841969
P-ISBN(Hardback): 9780821841969
Subject： O189.11 topological space (topological space)
Keyword： Analysis
Language： ENG
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The Mapping Class Group from the Viewpoint of Measure Equivalence Theory
Description
The author obtains some classification result for the mapping class groups of compact orientable surfaces in terms of measure equivalence. In particular, the mapping class groups of different closed surfaces cannot be measure equivalent. Moreover, the author gives various examples of discrete groups which are not measure equivalent to the mapping class groups. In the course of the proof, the author investigates amenability in a measurable sense for the actions of the mapping class group on the boundary at infinity of the curve complex and on the Thurston boundary and, using this investigation, proves that the mapping class group of a compact orientable surface is exact.