Framed cobordism of framed submanifolds

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Definition

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