Bones about 4-dimensional differential structures and about Seifert surgeries

我用Cork和Plug研究了四维流形的几种局部变形。我用我的无穷阶插头构造了无穷多个有边界的奇异结构。此外，我还考虑了其他各种引起奇异结构的变形。对于同调球面，我发现了一些负定的自旋4维流形。T.Abe和我研究了条带猜想，结果发现奇点集推广了带状奇点集。我们发现一些8_{20}的环扭曲给出了带状结。Y.Yamada和我做了晶状体空间手术的研究。我们分析了从环形纽结和Berge的VII和VIII纽结手术中得到的闭合4-流形。我推进了我的晶状体空间手术分类问题的研究。我建立了用连分数来证明透镜空间保证完备性的方法。K.Sato和我研究了负定4-流形中的不可定向亏格。

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.