what are the most interesting long standing problems in low-dimensional topology?

Question

What are the problem most interesting problems that people who do research in low dimensional topology have been working on in the past decade.

Answer 1

For a small list see here. For example, "The smooth 4-dimensional Poincare conjecture", or "Garoufalidis’s slope conjecture". For a nice survey on problems on low-dimensional topology, see here, from $2015$ in Kyoto. There is also a related MO-question.