Smooth embeddings of homologically similar manifolds

Roseman, Dennis M.

doi:10.1090/S0002-9947-1972-0310910-9

Smooth embeddings of homologically similar manifolds
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by Dennis M. Roseman

Trans. Amer. Math. Soc. 174 (1972), 107-126

DOI: https://doi.org/10.1090/S0002-9947-1972-0310910-9

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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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