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A classical result of simply connected surgery theory, is that if two normal maps $f:M_i\rightarrow X$, $i=0,1$ are normally cobordant and if the dimension of the manifolds is odd, there exists a ...

Let $N^n\subseteq M^m$ be a submanifold with a framing of the normal bundle, $2n<m$. Then $N^n$ is framed cobordant (in $M^m$) to something connected. I believe it could be proved by directly ...