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Suppose M 1 {\displaystyle M_{1}} and M 2 {\displaystyle M_{2}} are differential manifolds. A cobordism of M 1 {\displaystyle M_{1}} with M 2 {\displaystyle M_{2}} is a [[manifold with boundary ( N , ∂ N ) {\displaystyle (N,\partial N)} along with a diffeomorphism:
M 1 ⊔ M 2 → ∂ N {\displaystyle M_{1}\sqcup M_{2}\to \partial N}
