A group is the knot group of a surface-link, orientable or not, exactly when it admits a (2m,n)-presentation with inverses satisfying the weak ∂-condition, and an analogous statement holds for knot symmetric quandles.
Gonz ´alez-Acu˜na
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Characterizations of knot groups and knot symmetric quandles of surface-links
A group is the knot group of a surface-link, orientable or not, exactly when it admits a (2m,n)-presentation with inverses satisfying the weak ∂-condition, and an analogous statement holds for knot symmetric quandles.