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  "body": "\n## Summary\n\nTwo oriented [[knots|QYEAZTYGPT]] are concordant if they cobound a smoothly embedded annulus in $S^3 \\times [0, 1]$.\nConcordance is an equivalence relation, coarser than isotopy.\nThe concordance classes form an abelian group under [[knot sum|AGZSZW7GYE]], the knot concordance group.\nIts zero element is the class of [[slice knots|P68G28E4AD]].\n\n## Explanations\n\n### L1 human\n\nThink of time as a fourth direction, and let a knot move through time.\nDuring the motion it may change shape in ways that are not allowed in ordinary space, as long as the trace it sweeps out is a smooth tube without self-crossings.\nTwo knots are concordant if one can be turned into the other in this way.\nUnder this coarser notion of sameness, every knot has an inverse: its reversed mirror image.\n",
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