Various invariants of 3 and 4-manifolds and their applicationsUe

2019 Fiscal Year Final Research Report

• Project/Area Number: 16K05146
• 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, 理学研究科, 教授 (80134443)
• Co-Investigator(Kenkyū-buntansha): 加藤 毅 京都大学, 理学研究科, 教授 (20273427) ; 藤井 道彦 琉球大学, 理学部, 教授 (60254231)
• Project Period (FY): 2016-04-01 – 2020-03-31
• Keywords: 4次元多様体 / 3次元多様体 / Seiberg-Witten理論 / Floerホモロジー / ザイフェルト多様体

Outline of Final Research Achievements

We investigated the relation between invariants of 3-manifolds (in particular Seifert rational homology 3-spheres) which are defined combinatorially and those coming from gauge theories. These invariants are homology cobordism invariants, but other properties of them are mutually different. We heed further research about the relations between newly developed invariants and known results.
We almost completed writing the textbook about 4-dimensional topology written in Japanese, which includes
newly developed results about 4-manifolds as well as our own research results.

Free Research Field

3,4次元多様体のトポロジー

Academic Significance and Societal Importance of the Research Achievements

3次元多様体のホモロジーコボルディズム不変量は近年活発に研究されており，その研究をさらに発展させることは，4次元トポロジー，特に境界付き4次元多様体の性質の解明にとって有用である．
また4次元トポロジーの教科書は基礎理論から類書にない近年の研究結果までを含んでおり，この分野の研究を総合的に知る上で有用なものになることが期待される．