Normal and tangential structures (Ex)

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Let X be a connected n-dimensional finite Poincaré complex. Show that there is a natural bijection
\displaystyle \mathcal{N}_n(X) \cong \mathcal{N}_n^T(X)
where \mathcal{N}^T_n(X) is the set of normal bordism classes of normal maps to X with respect to the tangent bundle. (The proof is given in [Lück2001, Lemma 3.51].)

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