2021 Fiscal Year Final Research Report
The group structure of the mapping class group of a surface and its subgroups
Project/Area Number |
19K23409
|
Research Category |
Grant-in-Aid for Research Activity Start-up
|
Allocation Type | Multi-year Fund |
Review Section |
0201:Algebra, geometry, analysis, applied mathematics,and related fields
|
Research Institution | Tokyo University of Science |
Principal Investigator |
Omori Genki 東京理科大学, 理工学部数学科, 助教 (20843303)
|
Project Period (FY) |
2019-08-30 – 2022-03-31
|
Keywords | 写像類群 / 周期的写像 / 向き付け不可能曲面 / Dehn twist / Crosscap slide / 対称的写像類群 |
Outline of Final Research Achievements |
We gave Dehn twist--crosscap slide presentations for all involutions on non-orientable surfaces of genera up to 5. This work is a joint work with Naoki Sakata at Ochanomizu University. The BS mapping class group is the symmetric mapping class group for a periodic map on a oriented surface. We gave a finite presentation for the BS mapping class group by a joint work with Susumu Hirose at Tokyo University of Science. Moreover, we proved that the BS mapping class group is generated by three elements. The generating sets are minimal except for several cases.
|
Free Research Field |
位相幾何学
|
Academic Significance and Societal Importance of the Research Achievements |
曲面の写像類群は,その曲面をファイバーとする多様体のファイバー構造を介して,様々な次元の多様体のトポロジーと密接に関連しており,特にその中でも低次元多様体論において重要な役割を果たしている.その為,写像類群やその部分群の群構造に関する研究は,低次元トポロジーの発展に繋がる非常に重要な研究である. 本研究成果により,曲面が向き付け不可能な場合と向き付け可能な場合の両方の場合において,写像類群やその部分群の群構造の解明に寄与できたと考える.
|