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MR2653966 (2011e:57047) 57R40 (57Q37 57R52)
Skopenkov, A. Embeddings of $k$-connected $n$-manifolds into $\Bbb R\sp {2n-k-1}$. Proc. Amer. Math. Soc. 138 (2010), no. 9, 3377–3389.
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