论文标题
四局的pochette手术
Pochette surgery of 4-sphere
论文作者
论文摘要
Iwase和Matsumoto将“ Pochette手术”定义为在4个Manifolds上的剪切和paste，沿着4个manifold同型相当于$ s^2 \ vee s^1 $。 [10]中的第一作者研究了通过Pochette手术获得的许多同型4秒。在本文中，我们通过使用pochette嵌入的“链接数字”来计算任何同源性4-Sphere的Pochette手术的同源性。我们证明，带有琐碎绳索的Pochette手术不会改变差异类型或进行手术手术。我们还表明，在4球上存在具有非平凡的核心球和非平凡的绳索的Pochette手术，因此手术给出了4个球体。
Iwase and Matsumoto defined `pochette surgery' as a cut-and-paste on 4-manifolds along a 4-manifold homotopy equivalent to $S^2\vee S^1$. The first author in [10] studied infinitely many homotopy 4-spheres obtained by pochette surgery. In this paper we compute the homology of pochette surgery of any homology 4-sphere by using `linking number' of a pochette embedding. We prove that pochette surgery with the trivial cord does not change the diffeomorphism type or gives a Gluck surgery. We also show that there exist pochette surgeries on the 4-sphere with a non-trivial core sphere and a non-trivial cord such that the surgeries give the 4-sphere.
