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  "body": "\n## Summary\n\nA homotopy relative to a subspace $A$ is a [[homotopy|9YA6S6HD9V]] that keeps every point of $A$ fixed during the whole deformation.\nIt lets one deform maps while keeping a boundary condition, such as the end points of a path.\nPath homotopy, the fundamental group and deformation retractions are all defined with relative homotopies.\n\n## Explanations\n\n### L1 human\n\nImagine a rubber band pinned to a board at some points.\nYou may move the band, but the pins never move.\nA homotopy relative to $A$ is such a movement, where $A$ is the set of pinned points.\nFor example, two paths in the plane with the same end points can be deformed into each other with both end points held fixed.\n",
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