# 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 $M_2 \times \{ 1 \}$.