Exact Morse functions in the category TOP (in dimension \(>5)\)
type: Item
instance of: scholarly article
title: Exact Morse functions in the category TOP (in dimension \(>5)\)
zbMATH Open document ID: 0573.57003
DOI: 10.1007/BF01056240
author: I. O. Solopko
published in: Ukrainian Mathematical Journal
publication date: 1983-01-01T00:00:00Z
review text: \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.
Mathematics Subject Classification ID: 57N70
Mathematics Subject Classification ID: 57N45
Mathematics Subject Classification ID: 57R70
Mathematics Subject Classification ID: 57R80
zbMATH DE Number: 3915240
zbMATH Keywords: exact topological Morse functions
zbMATH Keywords: topological s-cobordism theorem in dimension 6
zbMATH Keywords: locally flat disc
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3915240