Oriented cobordism of oriented submanifolds

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Definition

Suppose M_1 and M_2 are oriented submanifolds of an oriented manifold N. An oriented cobordism from M_1 to M_2 is an oriented submanifold with boundary inside P \times I, that gives a cobordism between M_1 \times \{ 0 \} and M_2 \times \{ 1 \} (and such that the orientations match on the boundary).