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arXiv 1402.0801math.GTmath.SG
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4-流形上星形管道和奇异光滑结构的外科手术

Surgery along star shaped plumbings and exotic smooth structures on 4-manifolds

Cagri Karakurt, Laura Starkston

摘要:

我们定义了一个新的4维辛剪切和粘贴操作,这是类似于Fintushel和斯特恩的理性吹。我们使用这个操作来产生辛光滑奇异的复射影空间的多重结构,这些空间分别被放大八次、七次和六次。我们还展示了如何使用这种操作结合结手术,以构建一个无限的家庭最小的异国情调的光滑结构的复射影空间爆破七次。

英文摘要:

We define a new 4-dimensional symplectic cut and paste operation which is analogous to Fintushel and Stern's rational blow-down. We use this operation to produce multiple constructions of symplectic smoothly exotic complex projective space blown-up eight times, seven times, and six times. We also show how this operation can be used in conjunction with knot surgery to construct an infinite family of minimal exotic smooth structures on the complex projective space blown-up seven times.

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