Tubular neighborhoods of Hilbert cube manifolds

William Otis Nowell

Vol. 83 (1979), No. 1, 231–252

DOI: 10.2140/pjm.1979.83.231

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