Pochette surgery of 4-sphere
Tatsumasa Suzukia, Motoo Tangeb
- aDepartment of Mathematics, Tokyo Institute of Technology, Tokyo, Japan
- bInstitute of Mathematics, University of Tsukuba, Ibaraki, Japan
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Abstract
Iwase and Matsumoto (2004) defined "pochette surgery" as a cut-and-paste operation on 4-manifolds along a 4-manifold homotopy equivalent to S 2 ∨ S 1 .Suzuki (2022) studied infinitely many homotopy 4-spheres obtained by pochette surgery.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 nontrivial core sphere and a nontrivial cord such that the surgeries give the 4-sphere.Suzuki is supported by JST SPRING, grant number JPMJSP2106.
TL;DRIt is proved that pochette surgery with the trivial cord does not change the diffeomorphism type or gives a Gluck surgery, and the homology of pochete surgery of any homology 4-sphere is computed by using `linking number' of a pochettes embedding. (Semantic Scholar)