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 $$\mathcal{N}_n(X) \cong \mathcal{N}_n^T(X)$$ 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 \cite{Lück2001|Lemma 3.51}.) |
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== References == | == References == | ||
Latest revision as of 21:53, 25 August 2013
be a connected 
-dimensional finite Poincaré complex. Show that there is a natural bijection 
is the set of normal bordism classes of normal maps to with respect to the tangent bundle. (The proof is given in [Lück2001, Lemma 3.51].)
References
- [Lück2001] W. Lück, A basic introduction to surgery theory, 9 (2001), 1–224. Available from the author's homepage. MR1937016 (2004a:57041) Zbl 1045.57020
