| eBook ISBN: | 978-1-4704-0522-9 |
| Product Code: | MEMO/196/916.E |
| List Price: | $80.00 |
| MAA Member Price: | $72.00 |
| AMS Member Price: | $48.00 |
| eBook ISBN: | 978-1-4704-0522-9 |
| Product Code: | MEMO/196/916.E |
| List Price: | $80.00 |
| MAA Member Price: | $72.00 |
| AMS Member Price: | $48.00 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 196; 2008; 190 ppMSC: Primary 20; 37
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.
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Table of Contents
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Chapters
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1. Introduction
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2. Property A for the curve complex
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3. Amenability for the action of the mapping class group on the boundary of the curve complex
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4. Indecomposability of equivalence relations generated by the mapping class group
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5. Classification of the mapping class groups in terms of measure equivalence I
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6. Classification of the mapping class groups in terms of measure equivalence II
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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.
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Chapters
-
1. Introduction
-
2. Property A for the curve complex
-
3. Amenability for the action of the mapping class group on the boundary of the curve complex
-
4. Indecomposability of equivalence relations generated by the mapping class group
-
5. Classification of the mapping class groups in terms of measure equivalence I
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6. Classification of the mapping class groups in terms of measure equivalence II
