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  "body": "\n## Summary\n\nThe cobordism ring is the graded ring whose elements in degree $n$ are [[cobordism|T8BVGPPSZP]] classes of closed smooth $n$-manifolds.\nIts addition is disjoint union and its multiplication is cartesian product.\nThere are versions for unoriented, oriented, complex and other structured manifolds.\nThom computed the unoriented ring and showed that cobordism groups are homotopy groups of Thom spectra.\nThis brought homotopy theory into the classification of manifolds.\n\n## Explanations\n\n### L1 human\n\nTwo closed manifolds are cobordant if together they form the boundary of a compact manifold one dimension higher.\nFor example, two circles are cobordant, since they bound a cylinder.\nCobordism classes can be added by putting manifolds side by side and multiplied by taking products.\nThe result is a ring that records which manifolds can be turned into one another by such a filling.\n",
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