Cobordism
（重定向自Cobordism theory）
![A cobordism (W; M, N).](/Images/godic/202501/05/Cobordism.svg3100.png")
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![Fig. 1](/Images/godic/202501/05/Circle-surgery.svg3100.png")
![Fig. 2a](/Images/godic/202501/05/Sphere-surgery13100.png")
In mathematics, cobordism is a fundamental equivalence relation on the class of compact manifolds of the same dimension, set up using the concept of the boundary (French bord, giving cobordism) of a manifold. Two manifolds of the same dimension are cobordant if their disjoint union is the boundary of a compact manifold one dimension higher.