Research on low-dimensional manifold with handle diagram

2017 Fiscal Year Final Research Report

• Project/Area Number: 26800031
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: University of Tsukuba
• Principal Investigator: TANGE Motoo 筑波大学, 数理物質系, 助教 (70452422)
• Research Collaborator: ABE Tetsuya 立命館大学, 数理科学科, 数学嘱託講師 (00614009)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: エキゾチック微分構造 / コルク / ホモロジー球面 / スライスリボン予想 / レンズ空間手術

Outline of Final Research Achievements

In this research, I studied localization of exotic differential structures in 4-dimensional manifold. This phenomenon is due to the interesting existence of plug or cork. As a result, I obtained concrete construction of plug for Fintushel-Stern knot-surgery and its applications. I also constructed finite order Stein corks for the first time. In the later research, these corks have irreducible condition. Gompf constructed infinite order corks, I focus on some finite property for OS-invariants and generalized to the property which any infinite cork satisfies. In contrast to order two cork, this property is a remarkable nature. In the research of the Slice-Ribbon conjecture we found a close relationship between the slice-ribbon conjecture and handle theory. From the point of view, we give a sufficient condition for slice knot to be a ribbon by using a handle diagram with respect to the slice knot. The difficulty of slice-ribbon conjecture can rephrase the one of handle theory.

Free Research Field

低次元トポロジー