Involutions on spheres and Mahowald's root invariant
type: Item
instance of: scholarly article
title: Involutions on spheres and Mahowald's root invariant
zbMATH Open document ID: 0627.57024
DOI: 10.1007/BF01449218
author: Stephan Stolz
published in: Mathematische Annalen
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164403
review text: The author studies the question: For which pairs of homotopy spheres \((\Sigma ^ k, \Sigma ^{k+n})\) is there an involution on \(\Sigma ^{k+n}\) with fixed point set diffeomorphic to \(\Sigma ^ k ?\) It turns out that there is a necessary condition involving Mahowald's root invariant of the stable homotopy element represented by the fixed point sphere. Moreover if \(n>k+1\) and n,k satisfy certain conditions which guarantee the vanishing of the relevant surgery groups then this condition is ``almost'' sufficient, i.e. if the condition holds then there is an involution on \(\Sigma ^{k+n} \# \Sigma '\) with fixed point set \(\Sigma ^ k\), where \(\Sigma\) ' is a homotopy sphere bounding a stably parallelizable manifold.
Mathematics Subject Classification ID: 57S17
Mathematics Subject Classification ID: 57S25
Mathematics Subject Classification ID: 55Q45
zbMATH DE Number: 4020024
zbMATH Keywords: homotopy spheres
zbMATH Keywords: involution
zbMATH Keywords: fixed point set
zbMATH Keywords: Mahowald's root invariant
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4020024