Exact Morse functions in the category TOP (in dimension \(>5)\)
\textit{R. C. Kirby} and \textit{L. C. Siebenmann} [Foundational essays on topological manifolds, smoothings, and triangulations, Ann. Math. Stud. 88 (1977; Zbl 0361.57004)] suggested how one can prove TOP theorems on the h-(s-)cobordism, but this suggestion is relatively easily realized in dimensions \(>6\) [cf. \textit{T. Okabe}, J. Fac. Sci., Univ. Tokyo, Sect. I A 18, 23-35 (1971; Zbl 0214.224)], while in dimension 6 certain difficulties arise. They are expressed by the following question: let f: S'\(\to \partial W^ s\) be a locally flat embedding, and f is homotopic to zero in W, does there exist a locally flat disc \(D^ 2\) in W with \(\partial D^ 2=f(S^ 1) ?\) The proof of this lemma allows us to extend all results on exact Morse functions from the categories PL and DIFF (dimension \(>5)\) to the category TOP.
topological s-cobordism theorem in dimension 6
scientific article; zbMATH DE number 3915240