Orientation reversing involutions on Brieskorn spheres
type: Item
instance of: scholarly article
title: Orientation reversing involutions on Brieskorn spheres
zbMATH Open document ID: 0619.57017
author: Yasuhiko Kitada
published in: Kodai Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: The purpose of this paper is to classify the orientation reversing involutions on Brieskorn spheres of dimension \(4k+1\) which are defined by the conjugation of complex numbers. In this case, the fixed point set is of dimension 2k and to classify these examples, we meet with the failure of the ''gap hypothesis''. However, with the aid of \(Z_ 2\)-surgery theory due to \textit{K. H. Dovermann} [Michigan Math. J. 28, 267-287 (1981; Zbl 0491.57014)], this situation can be handled.
Mathematics Subject Classification ID: 57S17
Mathematics Subject Classification ID: 57S25
Mathematics Subject Classification ID: 57R67
Mathematics Subject Classification ID: 57R65
zbMATH DE Number: 4005169
zbMATH Keywords: orientation reversing involutions on Brieskorn spheres
zbMATH Keywords: conjugation of complex numbers
zbMATH Keywords: fixed point set
zbMATH Keywords: gap hypothesis
zbMATH Keywords: \(Z_ 2\)-surgery theory
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138037264
OpenAlex ID: W2039878154
cites work: Q5563921
cites work: Q5658847
cites work: \(Z_ 2\) surgery theory
cites work: Desuspendability of free involutions on Brieskorn spheres
cites work: \(O(n)\)-manifolds, exotic spheres, and singularities
cites work: Q5640470
cites work: Q3694282
cites work: Q3862116
DOI: 10.2996/KMJ/1138037264
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description: scientific article; zbMATH DE number 4005169