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  "body": "\n## Summary\n\nThe Thom space of a real vector bundle $E \\to B$ is its unit disc bundle with the unit [[sphere bundle|3VQ2V5HH3R]] collapsed to a point.\nFor compact $B$ it is the [[one-point compactification|0GWN3CMRK8]] of the total space $E$.\nThe [[Thom isomorphism|N685RXHDZX]] identifies its reduced cohomology with the cohomology of $B$ shifted by the rank.\nThom spaces of universal bundles form the [[Thom spectra|6H8AGEN6NY]] that compute cobordism groups.\n\n## Explanations\n\n### L1 human\n\nOver each point of the base there is a disc, the vectors of length at most one.\nThe Thom space glues the boundary circles or spheres of all these discs to one common point.\nSo each disc becomes a sphere, and all these spheres touch at the collapsed point.\nFor a bundle over a single point, the Thom space is one disc with its boundary collapsed, which is a sphere of the same dimension.\n",
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