## Trisections and link surgeries.(English)Zbl 1473.57052

Summary: We examine questions about surgery on links which arise naturally from the trisection decomposition of 4-manifolds developed by [D. T. Gay and R. Kirby, Geom. Topol. 20, No. 6, 3097–3132 (2016; Zbl 1372.57033)]. 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.

### MSC:

 57K30 General topology of 3-manifolds 57K10 Knot theory