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  "body": "\n## Summary\n\nThe relative homotopy group $\\pi_n(X, A, x_0)$ of a pair $A \\subseteq X$ consists of homotopy classes of maps of an $n$-disk into $X$ with boundary in $A$.\nIt is the homotopy analogue of relative homology.\nThe relative groups fit into a long exact sequence with the [[homotopy groups|P976WYEFMB]] of $A$ and of $X$.\nThis sequence is the main tool for computing homotopy groups of fibrations.\n\n## Explanations\n\n### L1 human\n\nA relative homotopy group counts disks in a big space whose rim lies in a smaller subspace.\nTwo such disks count as the same if one can be deformed into the other while the rim stays in the subspace.\nTake the disk $D^2$ with its boundary circle as subspace.\nThe identity disk cannot be pushed off, and the group is $\\Z$, counting how many times the rim winds around the circle.\n",
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