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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

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


Author: Rong Liu
Journal: Trans. Amer. Math. Soc. 347 (1995), 4245-4258
MSC: Primary 57N35; Secondary 55Q05
MathSciNet review: 1290732
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1995-1290732-0
PII: S 0002-9947(1995)1290732-0
Keywords: Embedding, isotopy classification, twisted Hurewicz theorems
Article copyright: © Copyright 1995 American Mathematical Society