2013 Fiscal Year Final Research Report
Research on generalized Dehn twists
| Project/Area Number |
24840038
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Tsuda College |
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Principal Investigator |
KUNO Yusuke 津田塾大学, 学芸学部, 講師 (80632760)
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| Project Period (FY) |
2012-08-31 – 2014-03-31
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| Keywords | 写像類群 / デーンツイスト / ジョンソン準同型 / ゴールドマン・リー代数 / テュラエフ余括弧積 |
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| Research Abstract |
Generalized Dehn twists are defined for loops on a surface which may have self intersections. Generalized Dehn twists suggest the importance of the self intersections of loops on a surface in the study of the mapping class group. The present project studied the mapping class group of a surface using generalized Dehn twists and the Goldman-Turaev Lie bialgebra, which is a notion behind generalized Dehn twists. Also it investigated the homological Goldman Lie algebra and fatgraph complexes, and obtained several results.
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