Equivariant isotopies and submersions
type: Item
instance of: scholarly article
title: Equivariant isotopies and submersions
zbMATH Open document ID: 0558.57015
published in: Illinois Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: In equivariant smoothing theory, one would like to make use of equivariant versions of the topological immersion, resp. submersion theorems due to \textit{J. A. Lees} [Bull. Am. Math. Soc. 75, 529-534 (1969; Zbl 0176.217)] and \textit{D. Gauld} [Trans. Am. Math. Soc. 149, 539-560 (1970; Zbl 0197.204)]. A G-immersion theorem is developed and used by the author and \textit{M. Rothenberg} in [Proc. Symp. Pure Math. 32, Part 1, 211-266 (1978; Zbl 0407.57018)]. The aim of this paper is the proof of an analogue G-immersion theorem: Let G be a finite group, N and Q be topological G-manifolds such that N satisfies the Bierstone condition - which already occurs in the smooth setting [see \textit{E. Bierstone}, Topology 13, 327-345 (1974; Zbl 0297.58005)]. Then the natural map from the simplicial set of G-submersions between N and Q into that of G- microbundle surjections of their tangent microbundles is a homotopy equivalence. The main ingredients of the proof are a G-isotropy extension theorem and a G-lifting theorem for submersions. These, in turn, are proved using the techniques of \textit{L. C. Siebenmann} [Comment. Math. Helv. 47, 123-163 (1972; Zbl 0252.57012)].
reviewed by: Martin Raussen
Mathematics Subject Classification ID: 57S17
Mathematics Subject Classification ID: 57N55
Mathematics Subject Classification ID: 57R91
Mathematics Subject Classification ID: 57N37
Mathematics Subject Classification ID: 57N80
Mathematics Subject Classification ID: 57R10
zbMATH DE Number: 3890379
zbMATH Keywords: topological G-manifold
zbMATH Keywords: equivariant submersions
zbMATH Keywords: equivariant smoothing theory
zbMATH Keywords: G-immersion theorem
zbMATH Keywords: Bierstone condition
zbMATH Keywords: G-microbundle surjections
zbMATH Keywords: tangent microbundles
zbMATH Keywords: G-isotropy extension theorem
zbMATH Keywords: G- lifting theorem for submersions
author: Richard K. Lashof
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3890379