Relations between invariants of low-dimensional manifolds and their geometric structures

2015 Fiscal Year Final Research Report

• Project/Area Number: 24540076
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Kyoto University
• Principal Investigator: Ue Masaaki 京都大学, 理学(系)研究科(研究院), 教授 (80134443)
• Co-Investigator(Kenkyū-buntansha): Tsuyoshi Kato 京都大学, 理学研究科, 教授 (20273427) ; Michihiko Fujii 京都大学, 理学研究科, 准教授 (60254231)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 低次元トポロジー / 3次元多様体 / 4次元多様体

Outline of Final Research Achievements

Ue studied invariants of 3-manifolds originated from the Seiberg-Witten and the Heegaard Floer homology theory. In particular in case of Seifert rational homology 3-spheres,which consist of special classes among 3-manifolds, he proved the mu-bar invariant (which is combinatorially defined) is represented by some combinations of analytically defined eta invariants under certain conditions using the Seiberg-Witten theory. He announced the above results at the conferences in Japan and overseas from 2012 to 2015 and completed the preprint (which is prepared to submit). He also continued to write a textbook on 4-manifolds, which started several years ago, including the latest achievements. He is trying to make the textbook in complete form within a year.

Free Research Field

微分位相幾何学，低次元トポロジー