On the classification of (𝑛-𝑘+1)-connected embeddings of 𝑛-manifolds into (𝑛+𝑘)-manifolds in the metastable range

Liu, Rong

doi:10.1090/S0002-9947-1995-1290732-0

On the classification of $(n-k+1)$-connected embeddings of $n$-manifolds into $(n+k)$-manifolds in the metastable range
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Trans. Amer. Math. Soc. 347 (1995), 4245-4258 Request permission

Abstract:

For an $(n - k + 1)$-connected map $f$ from a connected smooth $n$-manifold $M$ to a connected smooth $(n + k)$-manifold $V$, where $M$ is closed, we work out the isotopy group ${[M \subset V]_f}$ in the metastable range $n \leqslant 2k - 4$. To prove our results, we develop the Hurewicz-type theorems which provide us with the efficient methods of computing the homology groups with local coefficients from the homotopy groups.

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On the classification of embeddings of

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