Link concordance
In mathematics, two links L 0 ⊂ S n {\displaystyle L_{0}\subset S^{n}} and L 1 ⊂ S n {\displaystyle L_{1}\subset S^{n}} are concordant if there exists an embedding f : L 0 × [ 0 , 1 ] → S n × [ 0 , 1 ] {\displaystyle f:L_{0}\times [0,1]\to S^{n}\times [0,1]} such that f ( L 0 × { 0 } ) = L 0 × { 0 } {\displaystyle f(L_{0}\times \{0\})=L_{0}\times \{0\}} and f ( L 0 × { 1 } ) = L 1 × { 1 } {\displaystyle f(L_{0}\times \{1\})=L_{1}\times \{1\}} . By its nature, link concordance is an equivalence relation.