Refinement of Gauge Theory and 4-dimensional topology

2017 Fiscal Year Final Research Report

• Project/Area Number: 25400096
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Osaka Medical College (2015-2017); Gakushuin University (2013-2014)
• Principal Investigator: Nakamura Nobuhiro 大阪医科大学, 医学部, 講師 (10512171)
• Research Collaborator: ISHIDA Masashi 東北大学, 大学院理学研究科, 教授 ; MATSUO Shinichiroh 名古屋大学, 大学院多元数理科学研究科, 准教授
• Project Period (FY): 2013-04-01 – 2018-03-31
• Keywords: ゲージ理論 / トポロジー / 4次元多様体 / 山辺不変量

Outline of Final Research Achievements

We have mainly investigated and developed the Pin(2)-monopole theory for applications to 4-dimensional topology and geometry. The results of this study are as follows: 1.Computations and applications of the Pin(2)-monopole invariants. In particular, the connected-sum formula, applications to exotic structures and computations of Yamabe invariants. 2.Formulation and computations of stable cohomotopy invariants. 3.Pin(2)-moopole theory on 4-manifolds with boundary and applications to intersection forms with local coefficients. 4.Nonvanishing theorem for almost Kaehler surfaces with real structures.

Free Research Field

幾何学