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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Smooth embeddings of homologically similar manifolds


Author: Dennis M. Roseman
Journal: Trans. Amer. Math. Soc. 174 (1972), 107-126
MSC: Primary 57D40
DOI: https://doi.org/10.1090/S0002-9947-1972-0310910-9
MathSciNet review: 0310910
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Abstract: We consider the situation where we have two smooth n-manifolds $ N \subseteq M$ with $ {H_\ast }(M,N) = 0$ and show that given a smooth embedding of N into some manifold Q we may, under suitable conditions, extend this to embeddings of M into Q, $ Q \times I$, or $ Q \times {I^2}$ (where I is the unit interval). We can apply these results to obtain smooth embeddings of homologically k-connected manifolds into $ (2n - k + 1)$-dimensional euclidian space.


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DOI: https://doi.org/10.1090/S0002-9947-1972-0310910-9
Keywords: Homology n-connected, h-cobordism, homology cobordism, handle decomposition
Article copyright: © Copyright 1972 American Mathematical Society