Added gt.geometric-topology tag.
tagged open-problems-list, it implies poping-up this nice question -- hope this serves the community
|1||[made Community Wiki]|
What are some of the big open problems in 3-manifold theory?
From what I understand, the geometrization theorem and its proof helped to settle a lot of outstanding questions about the geometry and topology of 3-manifolds, but there still seems to be quite a lot of activity. I am not prepared to make a full push to familiarize myself with the literature in the near future, but I am still curious to know what people are working on, what techniques are being developed, etc.
So I was hoping people could briefly explain some of the main open questions and programs that are motivating current research on 3-manifolds. I'll let the community decide if this undertaking is too broad, but I'm hoping it is possible to give a rough impression of what is going on. References to survey articles are appreciated, especially if they are accessible to non-experts like myself.
It seems like the community wiki designation is appropriate for this question, and the usual rules ought apply.