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2016 Fiscal Year Final Research Report

Moduli theory of non linear elliptic operators over non compact manifolds

Research Project

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Project/Area Number 25287009
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypePartial Multi-year Fund
Section一般
Research Field Geometry
Research InstitutionKyoto University

Principal Investigator

Kato Tsuyoshi  京都大学, 理学(系)研究科(研究院), 教授 (20273427)

Co-Investigator(Kenkyū-buntansha) 木田 良才  東京大学, 数理(科)学研究科(研究院), 准教授 (90451517)
Co-Investigator(Renkei-kenkyūsha) Kida Yoshikata  東京大学, 数理科学研究科, 准教授 (90451517)
Oguni Shin-ichi  愛媛大学, 理工学研究科, 准教授 (00549446)
Fukaya Tomohiro  首都大学, 東京理工学研究科, 准教授 (40583456)
Tsukamoto Masaki  京都大学, 理学研究科, 准教授 (70527879)
Matsuo Shinichiroh  名古屋大学, 多元数理科学研究科, 准教授 (40599487)
Project Period (FY) 2013-04-01 – 2017-03-31
Keywordsゲージ理論 / 非可換幾何学 / モノポール写像 / 普遍被覆空間
Outline of Final Research Achievements

I have constructed a monopole map over the universal covering space of a compact oriented smooth four manifold. We apply the infinite dimensional Bott periodicity by Higson-Kasparov-Trout. In particular its degree was given when the linearized map is isomorphic, as an element in the equivariant E theory. It produces a homomorphism between K group of C* algebras related to the group ring. It corresponds to a covering version of the Bauer-Furuta degree.
As an application, we proposed an aspherical 10/8 inequality for spin classifying 4 manifolds. We have also verified that it certainly holds for large class of 4 manifolds which includes complex minimal surfaces of general type.

Free Research Field

幾何学

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Published: 2018-03-22  

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