Handle decompositions and smooth structures on 4-manifold
| Project/Area Number |
23840027
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Hiroshima University |
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Principal Investigator |
YASUI Kouichi 広島大学, 大学院・理学研究科, 助教 (70547009)
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| Project Period (FY) |
2011 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2011: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | トポロジー / 4次元多様体 / 微分構造 / ハンドル分解 / コルク / Stein多様体 / 接触構造 / プラグ |
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| Research Abstract |
The principal investigator studied smooth structures on 4-manifolds, using the diagrams of their handle decompositions. The main results are the following (1) - (3). The results (2) and (3) are joint works with Selman Akbulut (Michigan State University). (1) The principal investigator proved that a large class of 3-manifold bounds a 4-manifold which has infinitely many exotic smooth structures. (2) We gave a new sufficient condition under which a Gluck twist to a 4-manifold with odd intersection form does not change the smooth structure. (3) We constructed infinitely many simply connected Stein 4-manifolds with b2=2 that are mutually exotic. Moreover, they are Stein fillings of the same contact 3-manifold.
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Report
(3 results)
Research Products
(26 results)
