2013 Fiscal Year Final Research Report
Bones about 4-dimensional differential structures and about Seifert surgeries
| Project/Area Number |
24840006
|
|---|
| Research Category |
Grant-in-Aid for Research Activity Start-up
|
| Allocation Type | Single-year Grants |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | University of Tsukuba |
|---|
Principal Investigator |
TANGE Motoo 筑波大学, 数理物質系, 助教 (70452422)
|
|---|
| Project Period (FY) |
2012-08-31 – 2014-03-31
|
| Keywords | 4次元多様体 / 3次元多様体 / 結び目 / スライスリボン予想 |
|---|
| Research Abstract |
I studied some types of the local deformation of 4-manifolds by using Cork and Plug. I constructed infinitely many exotic structures with boundary by using my plug with infinitely order. Also, I considered other various deformation arising exotic structures. I found some negative-definite spin 4-manifolds for homology spheres. T.Abe and I studied slice-ribbon conjecture, as a result we found singularity sets generalizing ribbon singurality sets. We show the annulus twists for some 8_{20} gives ribbon knots.
Y.Yamada and I did research of lens space surgery. We analyzed the closed 4-manifolds obtained from torus knot and Berge's VII and VIII knot surgeries. I advanced the research of my classification problem of lens space surgery. I established the way to use continued fraction to prove the completeness of lens space suregery. K. Sato and I studied non-orientable genus in negative-definite 4-manifolds.
|
Research Products
(10 results)
