Research on smooth structures on 4-manifolds using handle decompositions

2015 Fiscal Year Final Research Report

• Project/Area Number: 25800048
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Hiroshima University
• Principal Investigator: YASUI Kouichi 広島大学, 理学(系)研究科(研究院), 助教 (70547009)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: トポロジー / 4次元多様体 / 微分構造 / ハンドル分解 / Stein構造 / 接触構造 / コルク / 結び目

Outline of Final Research Achievements

We gave an algorithm which produces infinitely many pairwise exotic (i.e. homeomorphic but non-diffeomorphic) Stein fillings of the same contact 3-manifolds. We also gave a method for producing pairs of framed knots which represent exotic pairs of 4-manifolds. As an application, we disproved the Akbulut-Kirby conjecture on knot concordance. We also obtain results on contact 5-manifolds and maximal Thurston-Bennequin numbers of knots.

Free Research Field

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