2011 Fiscal Year Final Research Report
On the relation between invariants of the mapping class groups
| Project/Area Number |
20740031
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
KIN Eiko 東京工業大学, 大学院・情報理工学研究科, 講師 (80378554)
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| Project Period (FY) |
2008 – 2011
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| Keywords | 写像類群 / 擬アノソフ / dilatation / エントロピー / 3次元双曲多様体 / 双曲体積 |
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| Research Abstract |
Let L(g, n) be the minimal entropy of pseudo-Anosovs defined on an orientable surface of genus g with n punctures. Tsai proved that for any fixed g> 1, L(g, n) is on the order of log(n)/n. Thus in particular, the number c(g, n):=n・L(g, n)/log(n) is bounded by a constant from above, which does not depend on n. We found a new family of pseudo-Anosovs with small entropy, defined on orientable surface of genus g with n punctures for each g> 1 and for infinitely many n's. By using theses examples, we proved that for infinitely many g's, the number c(g, n) is bounded by 2.
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