Cobordism of submanifolds

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Suppose M_1 and M_2 are submanifolds of a differential manifold P. A cobordism of submanifolds from M_1 to M_2 is a submanifold with boundary (N, \partial N) in P \times I, that provides a cobordism between M_1 \times \{ 0 \} and M_2\times \{ 1 \}.

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