2016 Fiscal Year Final Research Report
Construction of 4 dimensional manifolds using mapping class groups and its applications
| Project/Area Number |
25800043
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Osaka Electro-Communication University (2014-2016)
Tokyo University of Science (2013) |
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Principal Investigator |
MONDEN NAOYUKI 大阪電気通信大学, 工学部, 講師 (60611986)
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| Research Collaborator |
AKHMEDOV ANAR
R. INANC REFIK Baykur
HAMADA NORIYUKI
VAN-HORN MORRIS JEREMY
KOBAYASHI RYOMA
YOSHIHARA KAZUYA
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Keywords | Lefschetz fibration / Lefschetz pencil / symplectic 4-manifold / mapping class group / stable commutator length |
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| Outline of Final Research Achievements |
We studied Lefschetz fibrations and Lefschetz pencils, which play an important role in 4-dimensional topology, using mapping class groups. In particular, we solved a problem on the Euler characteristics of Lefschetz pencils and constructed explicit examples that their existence are known but there are no example or that they have new properties. Moreover, as an application of the techniques we obtained in the study, we gave a result on stable commutator lengths in mapping class groups.
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| Free Research Field |
幾何学
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