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  "body": "\n## Summary\n\nThe Whitehead tower of a space $X$ is a sequence of spaces $\\cdots \\to X\\langle 2 \\rangle \\to X\\langle 1 \\rangle \\to X$.\nThe stage $X\\langle n \\rangle$ is $n$-connected and has the same homotopy groups as $X$ above degree $n$.\nIt is dual to the [[Postnikov tower|EKGEZGHYBW]]: instead of discarding the high homotopy groups, it discards the low ones.\nIts first stage is the [[universal cover|Y1YPE6PM52]], and each further stage is a fibration over the previous one with fibre an [[Eilenberg–MacLane space|AJHEYJE5XY]].\nIt is used to compute homotopy groups with spectral sequences and to define string structures through the stage $BO\\langle 8 \\rangle$.\n\n## Explanations\n\n### L1 human\n\nThe Whitehead tower peels off the homotopy groups of a space from the bottom.\nThe first step replaces the space by its universal cover, which removes the fundamental group.\nThe next step removes the second homotopy group, and so on.\nEach stage keeps all the higher homotopy groups unchanged.\nFor example, the $3$-connected cover of the $3$-sphere has the same homotopy groups as $S^3$ in degrees $4$ and above, but none below.\n",
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