Diffeomorphism classification of finite group actions on disks
type: Item
instance of: scholarly article
title: Diffeomorphism classification of finite group actions on disks
zbMATH Open document ID: 0548.57022
DOI: 10.1016/0166-8641(83)90012-3
published in: Topology and its Applications
publication date: 1983-01-01T00:00:00Z
review text: Suppose a smooth G-manifold \((M^ k,\partial M^ k)\) is embedded in the n-disk \((D^ n,\partial D^ n)\). The reviewer studied the problem of extending this action from M to \(D^ n\) and the classification of such extensions [see Mem. Am. Math. Soc. 257 (1982; Zbl 0486.57015), Chapter VI, for a brief survey of the results in this direction]. The author proposes an alternative condition for the tangential data of \(M^ k\) when \(k=n\) and the action on \((D^ n-M^ n)\) is required to be free. He uses the \((\pi -\pi)-\)theorem of Wall to construct the extension and to classify the extensions, obtaining similar results to some of the results of \textit{W. Browder} and the reviewer (to appear in Trans. Am. Math. Soc., see op. cit.) which used thickening techniques.
Mathematics Subject Classification ID: 57S17
Mathematics Subject Classification ID: 57R67
zbMATH DE Number: 3874245
zbMATH Keywords: smooth G-manifold embedded in the n-disk
zbMATH Keywords: extensions of finite group actions
zbMATH Keywords: tangential data
author: Karl Heinz Dovermann
reviewed by: Amir H. Assadi
MaRDI profile type: Publication
full work available at URL: 0166-8641(83)90012-3
OpenAlex ID: W2023216460
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description: scientific article; zbMATH DE number 3874245