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Award ID contains: 1664587

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  1. We examine questions about surgery on links which arise naturally from the trisection decomposition of 4-manifolds developed by Gay and Kirby \cite{G-K3}. These links lie on Heegaard surfaces in $$\#^j S^1 \times S^2$$ and have surgeries yielding $$\#^k S^1 \times S^2$$. We describe families of links which have such surgeries. One can ask whether all links with such surgeries lie in these families; the answer is almost certainly no. We nevertheless give a small piece of evidence in favor of a positive answer. 
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