Let f : Xn→ Wn+2 be a
fixed embedding of manifolds, assume X compact, and let g : X → W be an
embedding close to f in the C0 topology. In general, g and f will not be
concordant. What small perturbation of g will yield an embedding concordant to
f?
In this paper, our goal is to replace g by a new embedding while altering the
image manifold g(X) as little as possible. In case X is simply connected, the problem
was solved by Cappell and Shaneson as follows: if n is odd, g(X) is already
concordant to f [5]. If n is even and f has trivial normal bundle, g(X) may be
replaced by its connected sum with a knot in W [4]. The current paper
applies previous work of the author [9, 10] to study the nonsimply connected
case.
