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2015 Fiscal Year Final Research Report

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

Research Project

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Project/Area Number 24540076
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionKyoto 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

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Published: 2017-05-10  

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