We consider the following question: when is the manifold obtained by gluing together two knot complements an $L$-space? Hedden and Levine proved that splicing 0-framed complements of nontrivial knots never produces an $L$-space. We extend this result to allow for arbitrary integer framings. We find that splicing two integer framed nontrivial knot complements only produces an $L$-space if both knots are $L$-space knots and the framings lie in an appropriate range. The proof involves a careful analysis of the bordered Heegaard Floer invariants of each knot complement.

中文翻译：

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拼接整数框结补码和有边Heegaard Floer同源性

我们考虑以下问题：什么时候通过将两个节点补码粘合在一起获得的流形是 $L$-空间？Hedden 和 Levine 证明拼接非平凡结的 0 帧补码永远不会产生 $L$-空间。我们扩展这个结果以允许任意整数帧。我们发现，如果两个结都是 $L$-空间结并且框架位于适当的范围内，则拼接两个整数框架的非平凡结补码只会产生 $L$-空间。证明涉及对每个结补集的有边界 Heegaard Floer 不变量的仔细分析。