Vol. 83, No. 1, 1979

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Tubular neighborhoods of Hilbert cube manifolds

William Otis Nowell

Vol. 83 (1979), No. 1, 231–252
Abstract

Let M and N be Q-manifolds and let i be a locally flat embedding of N into M. It is shown that if N = Q × Rn, then 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.

Mathematical Subject Classification 2000
Primary: 57N20
Secondary: 57N40
Milestones
Received: 3 March 1978
Revised: 5 July 1978
Published: 1 July 1979
Authors
William Otis Nowell