In mathematics, two links
are concordant if there exists an embedding
By its nature, link concordance is an equivalence relation.
It is weaker than isotopy, and stronger than homotopy: isotopy implies concordance implies homotopy.
A link is a slice link if it is concordant to the unlink.
A function of a link that is invariant under concordance is called a concordance invariant.
The linking number of any two components of a link is one of the most elementary concordance invariants.
The signature of a knot is also a concordance invariant.
A subtler concordance invariant are the Milnor invariants, and in fact all rational finite type concordance invariants are Milnor invariants and their products,[1] though non-finite type concordance invariants exist.
One can analogously define concordance for any two submanifolds
In this case one considers two submanifolds concordant if there is a cobordism between them in
This higher-dimensional concordance is a relative form of cobordism – it requires two submanifolds to be not just abstractly cobordant, but "cobordant in N".