Link concordance

In mathematics, two links ${\displaystyle L_{0}\subset S^{n}}$ and ${\displaystyle L_{1}\subset S^{n}}$ are concordant if there exists an embedding ${\displaystyle f:L_{0}\times [0,1]\to S^{n}\times [0,1]}$ such that ${\displaystyle f(L_{0}\times \{0\})=L_{0}\times \{0\}}$ and ${\displaystyle f(L_{0}\times \{1\})=L_{1}\times \{1\}}$.

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.