Smooth embeddings of homologically similar manifolds
Dennis Roseman · Transactions of the American Mathematical Society · 1972
We consider the situation where we have two smooth n -manifolds N ⊆ M N \subseteq M with H ∗ ( M , N ) = 0 {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 × I Q \times I , or Q × I 2 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 ( 2 n − k + 1 ) (2n - k + 1) -dimensional euclidian space.