TUBULAR-NEIGHBORHOODS OF HILBERT-CUBE MANIFOLDS

Let M and N be Q-manif olds and let i be a locally flat embedding of N into M. It is shown that if N = Q × Rnthen i must be flat. The following version of the Kirby- Siebenmann codimension 2 tubular neighborhood theorem is proved. If i is locally flat of codimension 2, then the embedded submanifold has a tubular neighborhood, and any two such tubular neighborhoods are isotopic. Among the tools developed is a relative version of Z-set unknotting. © 1979, University of California, Berkeley. All Rights Reserved.