Beyond Ribbon Concordance

Ribbon concordance has been proved to be a partial order system on knots and forms a complexity hierarchy. However, in this case, the knots are assumed to be in the three dimensional sphere. A natural question to ask is whether similar relations may be defined in 3-manifolds other than the three sphere. Since in general the fundamental group of 3-manifolds does not vanish, significant complexity different from the case of the three sphere is expected.

It's a interesting research topic.

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