2011 Fiscal Year Final Research Report
Structures of the cohomology rings of the Torelli group and Lagrangian mapping class groups
| Project/Area Number |
21740044
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Single-year Grants |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Tokyo Institute of Technology |
|---|
Principal Investigator |
SAKASAI Takuya 東京工業大学, 大学院・理工学研究科, 助教 (60451902)
|
|---|
| Project Period (FY) |
2009 – 2011
|
| Keywords | 位相幾何 / 写像類群 / トレリ群 / Johnson準同型 |
|---|
| Research Abstract |
Johnson-Morita theory plays an important role in the study of subgroups of mapping class groups of surfaces called Lagrangian mapping class groups. We determined the images of the rational fifth and sixth Johnson homomorphisms and studied the structures of related Lie algebras(Joint work with Shigeyuki Morita and Masaaki Suzuki). In particular, we determined the abelianization of so-called "the associative case" and showed that the highest rational homology group of the moduli space of Riemann surfaces vanish.
|
