Gompf 的软木塞和 Heegaard Floer 同源性

Pub Date : 2024-08-22 DOI:10.1093/imrn/rnae180

Irving Dai, Abhishek Mallick, Ian Zemke

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引用次数: 0

摘要

Gompf 证明，对于双捻结的某一族中的 $K$，燕式跟随操作会使 $K \# -K$ 上的 1/n$ 手术变成软木塞边界。我们推导出一个关于 $K$ 的一般弗洛尔理论条件，在此条件下，情况就是这样。我们的形式主义使我们能够进一步举出许多软木塞的例子，部分地回答了冈普夫的一个问题。与 Gompf 的方法不同，我们的证明并不依赖于任何封闭 4-manifold不变式或有效嵌入，而且还可以推广到其他差分变形。

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Gompf’s Cork and Heegaard Floer Homology

Gompf showed that for $K$ in a certain family of double-twist knots, the swallow-follow operation makes $1/n$-surgery on $K \# -K$ into a cork boundary. We derive a general Floer-theoretic condition on $K$ under which this is the case. Our formalism allows us to produce many further examples of corks, partially answering a question of Gompf. Unlike Gompf’s method, our proof does not rely on any closed 4-manifold invariants or effective embeddings, and also generalizes to other diffeomorphisms.

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